First off I think "aging" a beer to get rid of off flavors should be taken off any discussion about aging "good" beer. Those are really two different subjects.
I do notice that beers are different at all stages. I will sometimes taste wort and fermenting beer. I will taste when I take gravity samples, halfway through carbonation and as soon as it is carbonated. If the beer is not so good that I want to drink it every night until it is gone I might let it age some.
The flavor in a young beer and an aged beer are different. And as far as aging, I'm not going to pretend I have experience aging my own beers even as much as a year. To me the flavors in a beer aged months rather than weeks are usually "blended and smoothed" better. High alcohol content becomes less hot after aging and oaked beer becomes less "woody" with more vanilla.
Does every beer taste better if you keep it in your basement for 5 years? I'd have to think not.