When I did this for 4e, I called it "presumed competence". A level X character is presumed competent at thier abilities.
I didn't completely remove attributes. In 4e, your damage was (dice) plus (static modifier) -- I kept the static modifier from attributes to damage, and removed it from d20 rolls.
A version I've seen proposed in 5e is to use proficiency bonus.
Your Attack bonus is the
best of your attribute plus your proficiency, or twice your proficiency.
Your DCs is the
best of 8+attribute+proficiency, or 8 + 2*proficiency.
In effect, the floor of your attribute is your proficiency bonus.
An optimized attribute is usually 16 at level 1, 18 at level 4 and 20 at level 8+. Double prof vs attribute+prof is:
1: 4 vs 5
4: 6 vs 7
8: 8 vs 9
12: 10 vs 10
16: 12 vs 11
so failing to optimize your "attack" attribute costs you 1 point of DC or ATK modifier. And T4 characters get an extra +1 to hit regardless.
Your AC is either the base calculation, or:
Light armor: 10+proficiency+1/2 dex bonus
Medium armor: 10+proficiency+1/2 (max of dex or strength bonus) (+1 if stealth disadvantage)
Heavy armor: 12+proficiency+1/4 (sum of strength and con bonus)
round down the fractions, plus enchantment/shields/etc.
The bonuses from attributes cap out at +2, even if you have a belt of giant strength.
The 10+proficiency provides an AC floor, with a small contribution from an attribute on top, mostly for flavor: a 20s in attribute gives 2-3 points of AC over nothing at all, instead of 5.
Above 10+proficiency, the armor types give:
For light/medium we get:
10: +0 AC
14: +1 AC
18: +2 AC
For medium (stealth disadvantage) we get:
10: +1 AC
14: +2 AC
18: +3 AC
For heavy we get:
10/10: +2 AC
16/12: +3 AC
20/16: +4 AC
(note that with 10 con, you still get equal or higher AC from heavy than medium armor based off just strength)
This cap of +2 AC from higher stats is intended to exist, but not be so large as to make a huge difference.
---
By focusing on
hitting, the goal is to avoid the wiff. The stronger more dexterous will hit a bit harder, and gets more uses of some attribute-mediated abilities.
I'd leave all skills alone. If someone wants to wrestle a giant, invest in strength.
But DCs/ATK being too important to be left to chance seems reasonable, and rolling in an AC floor is also reasonable.
By having enchantment stack on top of this floor, and making the subtype of armor you wear stop mattering at higher levels, is an intersting side effect in my opinion.
A level 20 fighter in +3 plate armor and shield with 26 strength and 16 constitution has an "old" calculation of 26 AC.
Under the new calculation, they have 12 + 6 (prof) + (8+3=11/4 = +2 capped) + 6 +2 = 28 AC even if they are wearing +3 chainmail instead of +3 plate armor.
(That extra +2 AC might be a small problem; it falls out of wanting to ensure that light armor < medium armor < heavy armor AC, with each getting a +1 kick over the last. You could make light armor be 8+calc, medium with stealth disadvantage be 9+calc, and heavy be 10+calc instead.)