And of course the other direction to go, rather than removing scores or greatly reducing their impact, is to put a lot of effort into balancing them and making sure everyone has ways to use all of them.
I am not sure if everyone needs uses for each score, but 4E did some things you mentioned here
Every defense is the best of 2 scores. Reflex is the better of int or dex. (Armor bonus in light armor the same).
Will save is the better of charisma or wisdom.
Fortitude is the best of Strength or constitution.
Then in 4e subclasses (and their spells) were dependant on secondary ability scores.
So a barbarian screaming attsck might do additional area damage depending on charisma. A wizard spell might push enemies additional squares equal to your wisdom.
The monk had subclasses with different elements which were based on different secondary scores.
Then also some feats needed specific ability scores. Like dual implement caster (one of the strongest feats) needs 13 str and 13 dex.
So if we would want to just balance ability scores better there are for sure ways.
If we go into the other direction, then well saves could again just be good, medium or bad. And not depend on a stat. If attack does not increase with a stat then defense also can just be fixed.
(Instead of proficiency you could maybe just add level difference to enemy or rather GM could do that, this way higher level monsters still are stronger and lower level ones weaker).