Henry said:
Yeah, but then it's wasteful for a Fighter to have a High STR, when more levels make him hit better and with more damage, too.

In the scheme of things, CHA is slightly less useful than the other stats, but only marginally so.
I was just thinking about this topic. It's not wasteful, IMO, for a fighter to have high strength (maybe you were being sarcastic) and I think this is because:
1. the sheer volume of attack rolls made in a given game
2. damage roll is not based on level
Maybe charisma needs something like this in the mechanics. A roll to determine overall success or failure (the "to hit" roll) and then a roll to determine the degree of success.
For example: A PC walks up to a group of elves and tries to get them to join the party. The Diplomacy check determines whether or not the elves will consider the basic proposition. Success means PCs get consideration. Next, the actual task is considered and a straight charisma roll is made, determines if the elves will follow the PC through the gates of Hell, or just uncomfortably close. Maybe you roll a d8* for "impact" ("personality damage" ?). And so a low Diplomacy check means a miss, the elves aren't really even going to listen to what's being said, and there's no reason to determine it's "impact".
Here are some reasons (among many) why a DM might not like this scheme:
1. DMs like to determine reaction roll success based on story or PC actions exclusively.
My answer - you can't make a stat that affects random rolls important if you don't allow for those random rolls.
2. Some people don't like PCs with armies of henchmen and followers because it complicates the game.
My answer - if charisma is going to be important, you can't go limiting possible interactions with NPCs.
3. Too many dice rolls.
My answer - Two rolls, IMO is not too many, compared to the hours spent moving miniatures and rolling out the details of combat.
(* I like d8 better than d20 sometimes because I think d20 gives too wide a spread of numbers in some cases. I could win a surprising number of arm wrestling contests against a storm giant if we were both to roll d20 and add strength bonuses)