Let's break it down a bit more shall we?
What's wrong with my Cleric of Kord (god of Strength) using Strength as his casting ability? Would make a fair bit of sense, no?
Robin Hood is a perfect example of a charisma fighter - particularly the Erol Flynn version.
And, as far as "believability" goes, how is it possibly believable that my 8 Str 20 Dex archer is capable of accurately shooting a bow dealing gobs of damage when if we're going the "realistic" route, archers needed absolutely fantastic strength to draw those bows? Or, flip it around, my 18 Str 8 Dex great axe fighter is so skilled with swinging an axe that he is just as accurate and hits and deals just as much damage as that nimble 20 dex character using the same weapon?
The whole "I just can believe it" schtick is so overplayed and ludicrous on its face. We're right back to "I'll believe 6 impossible things before breakfast, but, that seventh, wow, that's just a doozy"
But, again, all this aside, I find it frankly astonishing that anyone would seriously argue that their preferences should be forced on other people in the group, let alone EVERYONE's table in the world. Just because someone doesn't find it plausible to have a Cha fighter means that people who don't even play at that table must not EVER play a Cha fighter?
Look, it's simple and it's the same thing that happened with ASI's. There are two options. The first option, someone gets to play the character they want to play but I don't. In the second option, everyone gets to play the character they want to play.
How in the world is option 1 even a consideration anymore?