Simple question, could a class that was nothing but ability score increases pass as a workable class? Like if every level you just gained a bonus ability point and no extra features. It would be a little boring for sure, but would it also be horribly broken?
It would have a few issues.
As to balance, the biggest issue with this design would probably be a form of the "jack of all trades, master of none" problem, where they don't do anything better than any of the existing classes. They don't damage, they don't heal, they don't have features that don't ping on ability scores. Put this guy next to a fighter, and he's going to have...better saves? That's about it. They'd be pretty good at any skill you'd care to mention, but a rogue would have higher results thanks to Expertise, and a Bard would be competitive. In a team environment, that class is not going to shine anywhere, because there's nowhere in particular for it to shine.
So it seems "weak."
My bigger concern personally would be about the
concept of the class, though. To me, classes are not just chassis for mechanics, they are identities in the world. A class like this doesn't have much identity - a single mechanic that isn't even an option that they can engage with in play isn't a great vehicle for pushing any identity you'd happen to want to stick on it, either.
Those would just be the biggest hiccups.
That said, you can count me as in the market for a "generic adventurer" class, too. But that's kind of my own pet itch.