Pitfalls of unlimited magic item creation:
Well, under a system like Pathfinder that doesn't charge XP for magic item creation, unlimited creation coupled with a free magic item market where things can be sold for market value provides a very easy way to generate lots of cash. At the very least, it lets you increase party wealth massively over standard wealth by level. We tried removing XP costs from crafting in 3.5 once, and by about 9th level we had twice as much magic gear as we should've.
Then there's the verisimilitude issue. Who makes all this crap? Why did some wizard spend 200 days out of his life making just this perfect +4 keen vorpal kama, investing 100000 gp worth of materials into a product for which there is a terribly limited demand? Why didn't he hire a company of pikemen and set himself up as a wizard king of some significant region of countryside with that money instead? Effectively, as a player and a GM, unlimited magic item purchasing freedom breaks my suspension of disbelief unless some very fast talking is done on a very regular basis. Eberron is one place where I might buy it because of the volume of artificers and magewrights and whatnot; not familiar enough with the Realms or Golarion to pass judgment there.
Consequences of restriction
Really where restrictions hit hardest is saving throws. There are lots of buffs that boost to-hit and let you punch through DR as though your weapon were magical; the options for general saves are rather more limited. Coming out of a 13th-level campaign where there were no Cloaks of Resistance to be had, I can tell you that it's a sad day when the pitiful 0th-level Resistance is a staple buff of 13th level characters (that and Protection from Evil, if we knew what we were going up against). But it was absolutely clutch to have; we went up against a bodak around 9th level, and I was the only one who bothered putting up Resistance and drinking a potion of Bear's Endurance. I was also the only survivor. Bad saves scale much more slowly than monster save DCs, and Cloaks of Resistance save lives. So, by opting for non-purchasable magic items, you can increase campaign lethality significantly. This may be desirable.
Additionally, if you keep handing out gold, players will be at a loss for what to do with it all. Then they'll start bribing magistrates and hiring mercenaries and buying ships and building castles and otherwise using money to interact with the world in a manner other than "buy these things that make my numbers better". If these are behaviors you wish to encourage, then restricting magic item purchases will help you achieve this end.
Kinds of games which benefit from unlimited magic item availability
Arguably, adventure-path type games and similar plot-heavy railroads benefit from it. Games where you don't want PCs dying left and right, and where you don't really want PCs to go out of their way to interact with the world (because that would damage plot), and where you likewise don't particularly care about the economic ramifications of allowing infinite availability. Combat As Sport games, where you want their numbers to be juuust right for them to fight your lovingly crafted encounters and not die. If that's the type of game you play, then unlimited availability is a great idea. It keeps everybody happy, and you don't end up with that one guy with the +4 sword that you rolled on the treasure tables while everybody else has +1.
Despite this, I still prefer to play and run games with limited magic item availability. If someone wants a Holy Avenger, they better go find a library and figure out what dungeon they can find one in, because they don't just have a rack of 'em at the general store. This generates player-driven quests, which I find to be generally more fun than DM-driven quests (be it via NPCs or circumstances). Likewise, I like my games reasonably-lethal, sans fixed plot and with as much player involvement with the setting as I can muster. Making magic items freely available for purchase at market price stifles all of these things.
The core Pathfinder rules for settlement demographics are in the PRD. It includes information on the highest level of spellcasting available in a settlement of each size. For example, in a large town (2001-5000 people) you can buy up to a 5th level spell. Even in a 20 person thorp you can get 1st level spells. This speaks to a certain level of commonality. If you want to flesh out a whole population, the 3.5e settlement rules had more thorough coverage.
There are however more Golarion specific rules in the Inner Sea World Guide p.253. To quote James Jacobs, Creative Director at Paizo, on the intent of this section from the Paizo forums:
I've always resisted nailing down exact numbers like this for NPC class levels, since I feel that it unnecessarily restricts adventure and sourcebook writing on the hobbyist and professional levels. Because once it's in print, folks tend to treat those numbers as sacrosanct; it's what happened with D&D, and as a result lots of people felt it was cheating to do something like have a super high level NPC live in a small town... which was already canon for a lot of places (such as Elminster living in Shadowdale).
The information on this topic I put into the Inner Sea World Guide is on page 253. It doesn't have MUCH to say, but it does break class levels down into four bands:
Standard (1st–5th level): This is where the vast majority of people are. It's very VERY uncommon to see NPCs with NPC class levels beyond this range.
Exceptional (6th–10th level): A significant number of national leaders and movers and shakers are of this level, along with heroes and other notables.
Powerful (11th–15th): These NPCs are quite rare; normally only a handful of such powerful characters exist in most nations, and they should be leaders or specially trained troops most often designed to serve as allies or enemies for use in high-level adventures.
Legendary (16th–20th): These are EXCEPTIONALLY rare, and when they appear they should only do so as part of a specific campaign; they all should be supported with significant histories and flavor.
Talk about percentages of the whole population never comes up in this section at al.
Also,
Once PCs get up above 13th level, they kind of ARE supposed to be the only ones who cans top the great evil. We want Golarion to be a world where the PCs are the heroes or the legends or whatever. Which means that most of the established groups of high level NPCs you'll see us create will be rivals or outright enemies, with high level good guys generally being loners or rulers of regions.
And
I'd be fine with saying 1 in 10 NPCs who have stat blocks that anyone would want to bother creating had some sort of spell-casting ability.
But the VAST majority of the humanoids in civilized areas should be commoners, aristocrats, warriors, or experts. Although there's a lot of magic in Golarion... I actually wouldn't call it "high magic." Folks still use lanterns and torches, not magic, to light most homes and city streets, after all.
You can look up various Golarion heads of state's class/levels on the Pathfinder Wiki.
Best Answer
My contention is - not much if anything.
History. All D&D settings are full of things done by ancient wizards or whatnot that are not actually achievable by PCs or NPCs under the normal game rules, whether it's the Field of Maidens or the Mana Wastes in Golarion or the Sea of Dust in Greyhawk or everything in the Forgotten Realms and Eberron. Using E6 for your PCs doesn't change that at all, so you don't need to retcon history to only account for "sixth level abilities."
Politics, Civics. First check out What percentage of the population is magical in Pathfinder's world of Golarion? Golarion is designed to not have many high level NPCs in the first place. Only people like country leaders are listed as higher level, or super-rare exceptional NPCs like Baba Yaga. You don't actually have to use the E6 rules for NPCs, so you could keep the most notable high level folks as their real high level and just make them super dangerous to cross for E6 PCs - a foe to plan a campaign around, not a mob to grind once the party's high level. Or, you can limit those rulers to L6 and rebuild them (where relevant) using the E6 rules. In that case the only political change I can think of is in cases where humans are collaborating with nonhumans (with the giants and winter wolves in Irrisen for example), devising a more nuanced justification for their cooperation than "a high level caster would melt the giants' faces if they misbehaved." So no real politic or civic changes except challenging you to find more textured explanations than "He in charge cuz he can bash everyone else."
Economy. Economy wise, there's less to spend megagold on since there's not super expensive items - but the inflation and problems of PCs having megagold compared to normal folks isn't good or conducive to a coherent game world anyway (see How to handle wealthy player characters as a GM?). The Golarion economy works better without the "hey there's a guy with 100,000 gp worth of stuff on him" problem.
Military. No D&D setting has ever had their militaries really reflect the realities of the D&D magic and combat system. They're always medieval-based theories of troops and fortifications that fly, invisibility, etc. make hash of. So there's not much to "dumb down" - the most notable "fantasy" units in Golarion are things like the Sable Marines of Korvosa who ride hippogriffs, which is still completely appropriate for E6.
Bestiary. Obviously you'd take a lighter hand with the high CR monsters just like the E6 rules say, but you don't have to remove them all - so a Linnorm King having to defeat a Linnorm is still on the table, it just means that the Linnorm Kings are way more bad ass than just being "a high level guy."
Adventures. The main problem with E6, really, is using the adventure content for Golarion. The Adventure Paths all go way past 6th level and chapters 3-6 would require significant adaptation, including the encounter tables and all. Since a big draw of Pathfinder/Golarion is the adventures, that's really the major downside. Also, if you limit all NPCs to L6 then your capstone threats can only be "monsters," which removes legendary threats like Baba Yaga, which is a bad GMing mistake IMO.
Frankly, E6 makes Golarion make more baseline sense than the usual d20 rules do! That's a big part of its draw; Golarion like Greyhawk and most traditional D&D campaign worlds are really only coherent if you assume there's not a bumper crop of high level folks around.