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?
I think it would be under powered as a single class.
However I also think it could be over powered as an option for multiclassing. Normally you have to take at least 4 levels of a class to get an ASI. But with this class, a quick dip nets you an ASI. I feel that it might be abused.
What else does it get? What is it proficient with? What is its die type for gaining HPs? If it gets 1d4 HPs per level and is proficient with nothing, then stat boosts every level is still probably going to be underpowered.
Twenty ASIs, assuming you take a +2 to a single stat every time, amounts to a +8 to 2 stats and a +6 to the other four stats. Bear in mind that stats max out at 20. Unless the DM is allowing feats as an option, some of those ASIs are probably going to go to waste.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.