So your issue is that ability scores matter?

Besides that, you got into a ton of stuff about scaling and the range of randomness, which we've already covered. If you want unexpected results to not happen, then you can't use a random element for your determiner. If you really don't like randomness, then just houserule that everyone takes 10 on all skill checks. Now the fighter will jump the same height every time, the wizard won't perform super-human feats some of the time, and all that other stuff that you mentioned.

Of course, you'll likely also have a player revolt on your hands, because all of the stuff you mentioned is secondary in importance to having a fun, balanced game.

If you have a better system you'd like to propose, that's fine, but I warn you that it'll likely get ripped apart by everyone here just like you've ripped apart the bounded accuracy system.

The object of good design isn't to eliminate all flaws, but to ensure that the flaws you have detract from the game as little as possible.