According to a regular in Gygax and Arneson's early Blackmoor and Greyhawk games, the cleric was largely draw from the priests in 70s vampire movies, with the prohibition against edged weapons inspired by legends and fantasy fiction:
Ahem. I was there.
In CHAINMAIL there were wizards that functioned as artillery.
Then there was Dave Arneson's first miniatures/roleplaying campaign.
Some players were 'good guys' and some players were 'bad guys' and
Dave was the referee.
One of the 'bad guys' wanted to play a Vampire. He was extremely smart
and capable, and as he got more and more experience he got tougher and
tougher.
This was the early 70s, so the model for 'vampire' was Christopher Lee
in Hammer films. No deep folklore [stuff].
Well, after a time, nobody could touch Sir Fang. Yes, that was his
name.
To fix the threatened end of the game they came up with a character
that was, at first, a 'vampire hunter'. Peter Cushing in the same
films.
As the rough specs were drawn up, comments about the need for healing
and for curing disease came up.
Ta da, the "priest" was born. Changed later to 'cleric'.
The bit about edged weapons was from Gary's reading the old stories
about Archbishop Turpin [ed: later clarified to be Bishop Odo], who wielded a mace because he didn't want to
shed blood ("who lives by the sword dies by the sword").
In other words, it came about the same way that 90% of the D&D rules
came about :
WE MADE UP SOME [STUFF] THAT WE THOUGHT WOULD BE FUN.
As he says, clerics were partly inspired by stories and misconceptions about historical warrior-priests, such as Turpin from the Song of Roland and Odo, a prominent figure in the Bayeux Tapestry. The idea of fighting clerics vowing to avoid spilling blood with their weapons is not at all historically accurate, but it's a popular image in some legends and Victorian pseudo-history, and featured in fantasy fiction of the 60s and 70s as well (e.g., according to Wikipedia, The Once and Future King).
As far as I can tell, there was no original rationale other than flavor. Maces are generally a bit weaker than swords in most editions of D&D, but OD&D used straight d6 for weapon damage rolls; I think at that stage the game had other "balancing" mechanisms so weapon damage wasn't a big one. I can't say whether Gygax actually believed the image of the cleric fighting with only blunt weapons was historical — remember, D&D's chief goal was always to emulate the creators' favorite fantasy fiction, not real history — but he clearly liked it enough to make it a part of the game.
Generally speaking, the damage type of a weapon is to do with how the shape of the weapon influences distribution of imparted force, rather than how you wield the weapon. 'Slashing' weapons have sharp edges, pointy weapons such as spears do 'piercing' damage, and staves, being blunt, are bludgeoning weapons.
That said, I'm guessing you've spotted that particular detail already. What you're asking about is where the line is drawn between one weapon type and another - after all, when you get right down to it, there's not a huge amount of difference between a very blunt spear and a very thin staff, right?
Well, I can't say for sure where that line is, but I do know this: Sling bullets, which are generally much smaller and less blunt than the end of a quarterstaff, do bludgeoning damage on impact. I take it from this that if you want to do piercing damage with a quarterstaff, you'll need to sharpen it into a spear, first - or have some obscure feat or magic that lets you do it, though I'm not aware of such a thing.
Best Answer
Nobody says they cant
But they are usually made of wood, as wood is much lighter than iron or steel. The heaviest of woods are between 74.4 lbs/ft3 to 84.5 lbs/ft3. While iron has a density of 491.5 lbs/ft3, and steel has a density of 483.81 lbs/ft3 according to Wikipedia. Both are at least six times heavier for the same dimensions.
And evidence of that is the Undine Weaponshaft, which is a mundane enhancement that can be applied to metal quarterstaves, spears and tridents (normally made of wood), it even says they can be made of special metal materials (mithril and adamatine). At the end of Ruby Phoenix Tournament module, there is an npc with an Adamantine quarterstaff. At the Council of Thieves adventure path, there is another npc with a bonded item that is a Mithral quarterstaff. At the Crucible of Chaos module (3.5) there is a magical staff, but this time made of Mithral.
According to the core rulebook on staves (the magical ones):
So, your typical quarterstaff (4 lbs) would weight at least 6 times as much (24 lbs), but its not impossible to be crafted. And also note that this is twice the weight of the heaviest weapons in the core rulebook (greataxe, halberd, guisarme, etc), and as such, why would anyone carry one of those for 1d6 damage if they could deal twice as much damage with an overall better weapon.
So when we read the rules about special materials saying a quarterstaff cannot be made of mithril/adamantine, it is talking about our typical quarterstaff.