I used to think that, until I sat down and actually tried excising ability scores from the rules. It's not so simple. The tentacles of ability scores snake into countless systems and it doesn't always work to use half your modified proficiency bonus. Each individual case is simple enough to resolve--but there are so many of them.
In particular, many systems depend on MAD to create distinctions or balance abilities. Armor class, for instance, is carefully engineered so that martial PCs will have high AC by default, while most casters have to work to get their AC up. That whole system falls apart if you take Dexterity out of the equation. Paladin auras go bonkers if they aren't forced to weigh Strength against Charisma (one of the knocks against the hexblade warlock is that you can dip one level and remove this balancing factor). Etc.
And, of course, there's the effect of Constitution on hit points. If you think hit point bloat is bad now, imagine what happens if every PC's Con modifier scales to +5 automatically for free.
As I said, each individual problem on this list can be resolved without a ton of work. But by the time you get done, you have a laundry list of house rules reaching into every corner of the game.