They most certainly dont and its a damn shame.Well no. It makes them closer to being equally important when building your character, but obviously not in play. And even then, you ran into issues-
Str gives you carry capacity. Con gives you healing surges and a few more hit points.
Dex gives you initiative. Int does not.
Cha gives you social skills. Wis gives you...Perception and Insight.
But I don't think any edition has ever managed to make all 6 ability scores equally viable. I mean, when I started playing in AD&D, Charisma didn't really do a lot by itself. Sure, it came up more at level 9 and up, when you're doing the base building thing (IF your game was doing that), and presumably it would matter if people were using the NPC reaction rules (which I never saw anyone use, but that's my own experience).
And it really hasn't gotten much better, other than, now there's incentive to have high Charisma for a few classes (technically Paladins and 2e Bards wanted Charisma, as well as a couple of specialty Wizards, but that was just a prerequisite, it didn't actually fuel any features).
Proficiency bonus matters more than ability bonuses even now, so it doesn't take much to be a face other than proficiency in Persuasion (and there's a few ways to get expertise on top of it).
To truly make all six ability scores equally useful, the game would have to use derived secondary characteristics, which is a layer of complexity I don't think the majority of D&D players want.