The Judge's Shield (1977) predates the Dungeon Master's Screen by about two years, give or take some months. (That the Judge's Guild got to this first is not surprising, as Gygax infamously told them that nothing but rules would sell, and the Judge's Guild was fated to prove him wrong.) So the term “shield” was established before the term “screen”, and still has minority currency today.

The Referee Screen (1979) for Traveller has the same vintage as the DM's Screen and is the only other data point before the 80s begin. It's unclear which was published first that year and therefore which one coined the term “screen”, but together with their two popular games — D&D and Traveller — they certainly had a large enough combined audience to establish the term “screen” in common usage over the the term “shield”, and likely TSR's audience alone would have been enough to establish the term as definitive. (Judge's Guild material, although designed for use with D&D and acclaimed at the time, was not “official” and that would have prevented a lot of play groups that didn't stray from TSR-branded material from being exposed to the alternate term.)

The history isn't very interesting, unfortunately. The only reason we have more than one word for it is because “shield” enjoyed first-to-market advantage in establishing mindshare enough to not be completely destroyed by the TSR juggernaut's adoption and promulgation of the term “screen.”

The “GM Screen” variation, as noted in the other question's answer, is merely a variation of the term that follows the separate trend of the hobby adopting “game master” as a non-trademarked, non-D&D-specific term, whether out of a hobbyist's need for precision or a publisher' need to avoid legal trouble. The term “GM screen” therefore doesn't have much of an interesting history of its own. You can see “GM screens” in a few early items:

• The Morrow Project's Game Masters Shield and Reference Tables (1980)
• The Star Trek Gamemaster's Kit (1983) including a “Gamemaster's Screen”
• Avalon Hill publishing the RuneQuest Games Master's Screen (1989) for RQIII

Deadlands: A Case Study in Metaplot

Deadlands is a "weird west" roleplaying game that started in 1996 and has had a pretty extensive metaplot, so it's a good case study as to why a metaplot exists. There are two major versions of it: the original Deadlands (often referred to as Deadlands Classic) and the Savage Worlds version Deadlands Reloaded.

To tell the story the author wants to tell

Sometimes, why a metaplot exists is as simple as "beacuse the author wants there to be one". There are a number of instances of this, but a pretty simple one is that Shane Lacy Hensley originally wanted to have a cataclysmic end to the Deadlands setting. When the game became unexpectedly popular, he created "a pretty cool story" to explain how it could still have that ending, yet keep going.

At first we were told that Westerns don’t sell, so we planned on a small print run, then we’d blow the world up and let the bad guys win—a story that would be told in the post-apocalyptic sequel, Hell on Earth. We did that, but as Deadlands proved successful we made it official that the Reckoners cheated…Hell on Earth wasn’t inevitable. Exactly how that works is best left to the books themselves, but we think it’s a pretty cool story. Short version? The Reckoners do lose and Hell on Earth is avoided—but then they cheat. At least in the official timeline.

Because fans enjoy it

Deadlands has a lot of characters and a number of stories. In Deadlands Design Diary #2, author Matthew Cutter described one of his missteps was killing off a number of beloved characters in the metaplot and underestimating fan love.

It wasn’t so much that they died. After all, Hell on Earth describes how Ronan Lynch’s skull ends up in future Lost Angels, so we know he had to go at some point. No, the problem was that they died off-camera, in a sidebar. Their deaths had no meaning or resonance. And in the end, my lack of history with Classic came back to bite me in the ass; I’d sorely underestimated the sheer amount of love for these characters.

He goes on to say that this was undone in errata, and that this lesson about how much fans cared about the metaplot heavily influenced writing the next major campaign.

Best of all, the fans taught me a very valuable lesson I could put to use on the next and final Servitor Plot Point.

To encourage players to buy more books

While I haven't seen a developer outright say that this was a reason, the books often encourage players to buy more books to learn about the "long story" overarching the Deadlands universe. The Deadlands: Player's Guide for Deadlands Classic started off the Chapter 1: Basics telling you that the game was linked by a metaplot spanning three separate RPGs, ending with encouragement to pick them up.

Welcome to the Weird West, amigo! This is one part of a long story told through three different roleplaying games. It all begins here, in the Weird West, where some say strange creatures called the Reckoners have begun “terrorforming” the world in fear.

The tale continues in Deadlands: Hell on Earth, a possible future where the bad guys have won. The villains’ efforts and the devastation of a supernatural nuclear war have turned the earth into a ravaged wasteland populated with horrible monsters and rugged survivors.

Deadlands: Lost Colony explores the outer space colonies left behind by the pre-holocaust humans of Hell on Earth. Isolated in the desolate and savage Faraway system, the colonists must contend with other desperate survivors and an incredible invasion of beings bent on their destruction.

All of these games are completely compatible, and should be available wherever you found this book (Deadlands: Lost Colony debuts in August 2000).

Some of the Deadlands Classic books were more blatant about it and said stuff like "such and such is a mystery, which we will reveal in Supplement Book X". I'll see if I can find one of these books.

To generate excitement for new products

In 2015, Pinnacle ran a Kickstarter for two products: the Stone and a Hard Place plot point campaign, and The Cackler graphic novel. The description for The Cackler especially highlighted the fact that it would change the Weird West forever.

Stone stalks the High Plains seeking heroes to kill. The Cackler hunts the Weird West in search of a mysterious girl called Rachel. Both of these killers are stone-cold dead...Harrowed...and what they're about to do kicks off the next era in the story of Deadlands!

The Cackler is an ancient Harrowed in search of a very particular blood relative for a nefarious and mysterious ritual that could change the world of Deadlands forever!

To reward longtime fans

That Kickstarter page for The Cackler challenged longtime fans to guess the secret identity based on clues from previous products.

Think you can figure out the Cackler's secret identity before you get to the end of the tale? We've been putting the clues out there for 20 years, amigo! (The most concise clues are in The Black Circle book for the original Deadlands Classic, by the way, but everything is retold right here in the graphic novel as well.)

To provide a story reason for a mechanical change

In Deadlands Reloaded, the Blessed, and their Voodooist variant, were an Arcane Background that worked pretty differently than any other Arcane Background. Pinnacle said in a rules update that they wanted to bring them more in line with the Deadlands spinoff settings and the core Savage Worlds.

As part of our ongoing effort to bring all the Deadlands settings’ rules in line with each other—and to better align them with Savage Worlds—here we introduce a few changes to the Weird West.

While they could have just changed them mechanically by fiat, they decided that the metaplot event "The Cackler" would be a good way to incorporate a story reason to explain these mechanical changes. This-out of-universe explanation was immediately followed by a header and an in-universe reason.

It’s tough to predict all the ways the West will change “After the Cackler”...but you can incorporate these two new Arcane Backgrounds and a Weird Edge into your campaign right away, Marshal.

Fans familiar with Deadlands Noir will notice these rules are similar to those of that setting. Read carefully though, as there are some differences. Even the Cackler can’t make the Weird West as bad as the Great Depression!

The Blessed

The forces of good lose a great deal of influence in the world After the Cackler, with their chosen no longer able to call down miracles like they were goin’ out of style. That being said, good’s chosen warriors aren’t without their particular advantages. [...]

Voodooists

As faith begins to wane After the Cackler, those voodooists who rely on the traditional, ritualistic practices find their magic still works. Traditional voodoo rituals, like those of Indian shamans, appease the spirits, allowing houngans and mambos to draw power from the Hunting Grounds. Other voodoo practitioners aren’t so lucky... [...]

Note that this rules update also contained mechanical changes to the "Harrowed" archetype, but there was no story reason incorporated with those changes.

To tie in with developments with spinoff materials

In the late 1990s, Pinnacle Entertianment Group created a partnership with AEG in which they would create several spinoff games for the Deadlands RPG. The most notable of these was the trading card game Deadlands: Doomtown, which centered on the town of Gomorra (nicknamed "Doomtown").

The RPG fully embraced this with supplement books Doomtown or Bust! and The Collegium. Since that game had its own metaplot, the main RPG metaplot incorporated it.

Compare with: Forgotten Realms novels, Shadowrun video games

To deal with real-world legal issues

AEG and Pinnacle eventually parted ways, and this led to an awkward situation. Pinnacle owned the rights to Deadlands, but Gomorra started in the card game and AEG owned the rights to it and the characters within. Since it was already integrated with the RPG, Pinnacle had to do something to explain its absence. So they said that an unexplained event blew up the town and nobody knew what really happened. The end.

Eventually, the two companies were able to work things out (likely as a result of the partnership from the sequel card game Doomtown: Reloaded), so a new adventure Sawed 'em in Gomorra was created to provide a more satisfactory metaplot resolution.

To make players feel like their actions have long-term consequences

Say that you are playing a Dungeons & Dragons scenario in something like Greyhawk. You kill a big, bad evil wizard who is threatening to destroy the world, but ultimately, your actions are inconsequential. Whether you win or lose, Greyhawk is exactly the same as it was before.

Some settings, such as Torg, Deadlands, and Spycraft have had adventures that had the potential to make a major change in the setting. For instance, Deadlands had an adventure called "Ghost Busters" where a major NPC in the setting was possessed and the players ultimately had to make the decision to kill him, or try to free him. The scenario had a card in the back of the book that you could tear off, where you marked what the fate of that character was and then mailed it in. After a certain date, all of the mailed in responses were tallied and the majority response became "official". The particular fate of that character has been referenced in future settings.

See Has "write in to impact the metaplot" been tried since the 90s? for more information

Deadlands Reloaded has done something similar. They have created four "Plot Point Campaigns" centering around four of the major NPCs in the Weird West, with the promise that each campaign will have a lasting impact on the setting. For instance, the first one The Flood ends with

The death of a major big bad in the setting at the hands of the players, which results in a major faction that has been around since the beginning collapsing.

The benefit to the players of The Flood is that they feel that their campaign had meaning.

Reasons from Other Settings

Forgotten Realms: To stay in line with changes to the core D&D rules

Fourth Edition D&D changed a number of rules systems in general, including how magic behaved and what races were more common. The metaplot for Forgotten Realms had an event called the "Spellplague", which brought the setting more in line with the default 4e setting. Unsurprisingly, the effects of the Spellplague were largely undone by the Second Sundering, which brought the setting more in line with 5e.

Shadowrun: To keep up with real-world changes

Back in the 1980s when Shadowrun was introduced, it seemed logical that the primary way to interact with computers would be to "jack in" to them. Then wi-fi became prevalent in the real world, so this seemed a little silly. While some people have preferred this archaic aesthetic (hence why Shadowrun periodically releases stuff set in the original year of 2050s), others got hung up on the future not having technology that we currently have today.

So the metaplot was changed to include story reasons to make wireless computer access available, and why it was less common in the past.