If we absolutely have to stick to six stats (personally, I think fewer, four or maybe five, would be better) then I think we should merge Constitution and Strength (call it "Might"), turn "Wisdom" into Perception, and fold the intellectual part thereof into Intelligence and the "I can't be dominated" part thereof into Charisma. Then Dexterity can be split into "Quickness" or something similar, covering just Initiative, Acrobatics, and what we currently call "Dex saves", while "Precision" or just "Dexterity" covers fine-detail movement (Thievery, AC, hit/dmg with Finesse, etc.)
With that, you've finally got a recipe for stats where each one is still pretty powerful and nobody really wants to dump any of them. Precision is really the only one that doesn't have something kinda important attached to it, since anyone not using finesse weapons or medium/light armor doesn't really care.