It tips balance towards multiclassing

Delaying the ASI or feat bonus is one of the detriments of multiclassing. It balances out the benefits of multiclassing.

Giving ASI or feat for every 4 total levels incentivises multiclassing, and steps on the toes of the fighter class that gets an extra ASI at level 6.

Multiclass Comparison

Consider something simple and melee oriented such as a level 4 fighter. Compare to a fighter 2 barbarian 2 and fighter 2 barbarian 1 rogue 1.

The system you propose obviates the class feature at level 4.

• The fighter 4 alone will have features from 3 levels, plus one ASI.
• The fighter 2 barbarian 2 will have features from 4 levels plus one ASI.
• The fighter 2 barbarian 1 rogue 1 will have features from 4 levels plus one ASI.

This allows gaining features without sacrificing the cost of ASI or feats.

Multiclasse

To reward/incentivize AGAINST multiclassing. This way you have more options on quando to multiclass, instead of just which class to choose. It also makes it tougher to add multiple classes that require different minimum ability scores.

If I allowed my players to get an ASI or feat every 4 character levels, how would the game balance be concretely impacted?

I think if they are solo class'd it wouldn't be a change at all, and unless they get really crazy into multiclassing it wont really be much of a difference. But it will absolutely lead to stronger PC's than the system intends.

How could the players abuse this?

They could conceivably create class combinations that are limited by the minimum ability scores under the normal rules which, while likely a lot of whacky fun, could lead to very strong combos. The system is that way to limit some of this because you likely have a deficient ability score somewhere to stop you from taking a bunch of classes/dips.