While I would normally just automatically agree with your statement, that, "People should be equally good at what they specialize in. So fighters should be as good at fighting as rogues are at sneaking and casters are at blasting at ALL levels." I am willing to say 'No, I do not automatically agree.'
Here's why.
Unless *all* enemies/challenges are *exactly the same* it's impossible for, say, "Sneaking" to be *equally effective* at all points in time in the game. Because of different HP values on enemies, "damage" is not *equally effective* vs all enemies. And so on. Because of that, it is *impossible* for sneaking to be "as good as" "fighting" or as good as "blasting" or anything else. Different challenges should test the limitations and specializations of PCs in different, and therefore, unequal ways.
My personal preference is for situational specialization to be a driving factor in "overwhelming goodness". I would prefer for fighters to be better than everyone else if it's a challenge that fighters should excel at. Same ways with all other classes. As long as there are enough different challenges so that everyone gets an equal amount of time, effectively, "being overpowered compared to the rest of the group" that's something that I would, in fact, enjoy.
Equality in Inquality, to go all Orwellian on your ass.
That's sort of what you're saying, but not exactly what you're saying I believe.
I think that what you're saying is more like 4th edition where everyone is "basically" exactly the same. The thing is, in 4th ed, all the "challenges" are effectively the same - deal damage to monster - period.
I don't want that kind of gameplay experience. Personal preference, of course.