Most significantly, at character/campaign creation. You can look at different mechanics and see which ones appeal to you, try something new and different, or hang particular role-playing quirks off of the mechanical quirks.
And then, at least in 3e, every time you leveled up (though, practically, that could have stood to be improved).
This is a flaw of individual effects, yeah. But it's not a flaw of including dramatically different PC abilities. Which is part of the baby-bathwater thing. You can improve on what 3e had without making everything work under the same umbrella mechanics. And you should.
I am probably misunderstanding you, but it sounds to me like you're saying that distinct mechanics are good not because they give more choices during the game but simply because distinct mechanics are good?
In practice didn't 3e result in a lot of class mechanics that made playing a character an exercise of following a certain rote in every combat? Do you really think it is preferably to have a system where each character has meaningful options in every encounter?
I think I'm starting to understand one problem for the acceptance of D&D:
When thinking about playing a game, we think (dream) about all the characters we would like to play. It is fun to imagine different types of characters and the more distinct such dreams are supported by a game, the more fun we have thinking about playing in such a game.
D&D doesn't seem to support many such dreams, especially to players with little experience with the system, to whom the abilities seem very uniform.
When actually playing in a game, we play the same character for a long time. So having a wide range of things to do with that character in game is more important than which other cool character I could play.
I guess this is an other example how D&D plays better than it reads.