In the original D&D game, Charisma was perhaps the second most important score (after Hit Points). Besides providing modifiers to NPC reactions, it limited the number of "henchmen" one could have and affected their morale and loyalty. As henchmen could gain experience levels, they were quite valuable assets if carefully cultivated.
If memory serves, that held true (by the books) in every TSR edition. Players did themselves (and DMs did Charisma) a disservice by neglecting that aspect of the game. If it was dropped from the rules in
3E, then the new designers can take some blame for making Charisma a "dump stat".
In Traveller, Social Standing sometimes serves a Charisma-like function. However, "dumping" is not relevant when scores are randomly generated rather than assigned by the player. There is also the twist that a low score might in some circumstances (to which adventurers are prone) be more advantageous than being an aristocrat. (Those do not include getting a commission in the Navy, though!)
In RuneQuest (old editions, anyhow), Charisma not only has a leadership component (less defined than in D&D) but is useful in such important matters as obtaining training. An interesting note is that the score can rise and fall depending on the success or failure of ventures.
That general idea seems to me quite good. As an indication of prestige, Charisma can have great appeal for players. Just knowing that his other stats make a character Hal the Hero -- for all that to the public he's a "zero" -- may not be as "cool" as getting acknowledgment, respect, deference, or even adulation.
Charisma could have additional value if it governs not only influencing others but also
resisting persuasion. That goes, though, against the general rule that players have free rein to choose their characters' responses.
I think the bottom line is that it really depends on how important interpersonal relationships are in the game. If the player-characters are all loners and social outcasts, then it might be as well to "dump" the rating from the game altogether.