Again--5e isn't THAT much different. Yes, a Fighter "can now do damage"* etc., but the vast, vast, vast majority of characters are going to fall within reasonably predictable ranges. Because most people aren't interested in weirdo tricksy "I literally cannot do damage ever" builds or the like. Things would be looser, but they wouldn't be useless.
And I think you seriously overplay the problems with solos. They were harder to balance than other things, yes. The same is true of 5e--to the point that they had to kludge in getting several "nope, that didn't happen" points (Legendary Resistance) and other such things. If problem A is present either way, but problems B-F all get addressed in one way or another by method 1 and not by method 2...well, you do the math.
*They never couldn't. Roles as straightjackets has always been a pernicious myth. But people cling to it nonetheless, so some lip service to their false beliefs is warranted.