Bilbo and Frodo had Sting. Aragorn had Anduril, Flame of the West. Elric had Stormbringer. I could go on.
Wolverine has claws, Ichigo has Zangetsu, Li-Mu Bai had the Green Destiny Sword...
I'm sure these characters would have been just as thematic if Bilbo and Frodo had to deal with Stormbringer, Aragorn had triple claws that went *SNICKT*, Elric had Sting, Wolverine had Anduril, Flame of the West, Ichigo had the Green Destiny Sword, and Li-Mu Bai had Zangetsu.
There's a difference, I think between building a character concept that starts with an integral weapon, for example, and a character concept that requires somewhere along the way for the character to gain this item. But more importantly, it is something that I wouldn't want in the games I run, at least insofar as having a player say "I want twin flaming scimitars" but in game a pair of flaming scimitars showing up in the next level appropriate horde. If the player (and his character) really want a pair of twin flaming scimitars, I'm more than happy to provide them in the context of the setting (the great dervish demon slayer of the past used them and now they are buried with him in his grand tomb, or whatever). But it is up to the player to go get them (and convince the rest of the group that it will be worth their while to accompany him).
To be honest, I am far less a fan of the setting being "level responsive" to the PCs than I am to accomodating players in achieving certain goals or even finding certain items. If Jade Jaws the green dragon that lives in the Big Wood is an ancient wyrm, he's an ancient wyrm whether the PCs go pester him at 20th level or 1st. If the King of Long-goninia had a Vorbal Hackmaster +12, that's what's to be found in his tomb, regardless of whether the item is "too powerful" for the PCs when they find it. Relatedly, if the random treasure table comes up with a +1 scimitar when the group's fighter is specialized in the long sword, it remains a +1 scimitar. If the fighter wants a magic longsword, he'll have to go find one or wait for the dice to favor his character generation choice.
(As a quick aside, i always thought this was a good balancing mechanic for the exotic and often superior weapons -- they were less likely to show up on the random magic item chart.)