so you got great stats randomly, meaning you probably have the best stats of the party. Then you are going to compound that difference by building a power-gamer's PC.
People rolling great stats building suboptimal characters is a great way to "even out" the party and remove some of the sting of rolling bad stats and ensure intra-party imbalance. Maybe I'm missing your point, but it seems like what you are proposing would make things worse, not better...
I think I agree with this some.
Usually I have a thematic idea in mind already and good stats let you play a weak class without suffering the same kind of debilitation. However if I did not want to play that weak class/subclass/race, I would not want it regardless of my stats.
I also don't see evening out as much of a problem in the games I play. Most players are happier when their colleagues are powerful. What I mean if you look at most tables and you are giving the option of a new player showing up with an average character or an awesome character, most tables would rather have the latter.