Exactly that.Genuine question because I'm feeling a bit dumb at the moment: how would you divorce the two? Are you talking about going back to a BAB/THAC0 deal where your to-hit is based more on your class than on your stat? Or do you mean something else?
There's a lot of ways you could implement it. The simplest one I've actually used is that you can always use your proficiency bonus in place of your stat modifier for attacks/damage/spell saves if the proficiency bonus is higher. So your attack bonus would have a floor of +4 at level 1, a +6 at level 5, a +8 at level 9, etc. It makes having a higher stat a bonus if you have it, but eventually it gets eclipsed by the proficiency bonus (unless you have a belt of cloud giant strength or something), and it makes playing a non-Str or Dex fighter or a non-Int wizard totally viable.
This makes assigning your stats become based on prioritizing skills or saves or just concept, which I feel is a better approach. Not tying a class to a "prime requisite" stat allows for a more freeform approach to character building.