A lot of this doesn't fit with my experience.The Encounter system generally assumes a balanced party, aka, a party made up of various classes that play off each other in some form of coordination but in practice most campaigns don't really get that. Your always going to end up with an adventuring party with shortcomings unless they really coordinate their character creation.
More to the point though roleplaying game balance in general is a very obtuse thing, what any single individual considers balanced or unbalanced is debatable. The only true form of balance D&D ever got was in 4e, in that the classes where balanced by effectively being equal within their archtype. So it didn't matter which striker or tank you chose as long as you had one so getting a balanced group, at least the discussion among players would be like "Im going striker... ok I'll go tank, ok I'll go control" and boom you have a perfectly balanced party. That was one good element of 4e. Problem with it was that it was incredibly boring in practice because as it turns out.. balanced roleplaying games are quite dry and boring.
Then there is the whole concept of in and out of combat balance... a barbarian polearmer is an awsome fighter, but outside of combat he is outright useless.
For instance, why would a polearm barbarian be useless out of combat? S/he will be strong, which can help with lifting/carrying things; s/he might well have a good CON, allowing for running long distances or performing other feats of endurance; and there is no reason why s/he should have a terrible CHA. The polearm fighter in my 4e game is not useless out of combat, and I would think that in a bounded accuracy environment like 4e that character would have an even wider range of viable non-combat action declarations.
I also think you are exaggerating the sameness of classes, and hence the relationship between capability and balance. In 4e a ranger and a sorcerer, for instance, play very differently; and I suspect that in 5e the experiences of playing an archer fighter and a blaster wizard or sorcerer will also be pretty different. When it comes to balance within a party, I think a lot of it is down to the group "making its own luck", and working well with what they bring to bear, rather than relying on some notionally optimal or balanced distribution of capabilities.