I've wanted this since Civ V. No need to go that in-depth, just mix-and-match existing bonuses (and, ideally, things like agenda and favored religion) and choose your own name, colors, symbol, and leader and background art (heck, you can't even rename your civ in this version of the game). Even being able to change the names and colors would be nice (for example, I liked Egypt's bonuses in Civ V, but I could never bring myself to stare at that eye-assaulting magenta-on-yellow for so many hours).
If balance is an issue, just add an option to disable custom leaders that's turned on by default in multiplayer (though you should still be able to customize purely aesthetic things like name and color).
As an added bonus, if two people wanted to play the same leader in multiplayer, letting one choose a different name and leader art would eliminate the confusion of having duplicate leaders running around.
I can see how mixing and matching abilities might be a fun exercise in over- or under-poweredness, but mods are sufficient for this. It's too niche a feature for the developers to go to the trouble of implementing it.
Only if you're a modder, which most people aren't; otherwise you can't do anything but hope the exact mod you want comes out.
And talking like being overpowered in single-player is a problem is pointless because the game already contains easy difficulties where every human-run civ is overpowered (not to mention you can do things like have Kongo as your only opponent with all victories disabled but religious). Heck, even older games usually contained cheat codes. If other people want unbalanced singleplayer games, how's that anyone else's business (and if it's achievements you're worried about, they could just disable achievements for custom civs, though there are already easy ways to cheese the "win on difficulty X" achievements, and most of the others can be obtained on the easiest difficulty)? And as for being underpowered, well, then all of those people who find deity too easy might finally be able to give themselves a challenge.
So many people want different civs that Firaxis can't possibly include them all. With mix-and-match, you could make whichever civ you wanted. I'd rather buy an expansion that let me mix-and-match my own civs (or even reskin existing civs) than one that contained five new leaders, because that way I can have all the leaders I could ever want (and there are already plenty of abilities to choose from), including ones neither Firaxis nor the modders would be likely to ever make.