CapnZapp
Legend
I let the player choose between Strength and Charisma.I feel Intimidation is ALWAYS a Charisma check.
You don't need to be the face guy (=put points in Charisma) to "persuade" people to cooperate. You don't need to be eloquent or witty in order to threaten people with extreme amounts of pain unless they do what they're told.
I understand intimidation is a kind of "presence", but requiring you to put points in Charisma means you become good at lots of other stuff. And you shouldn't need to be good at holding speeches or smooching the ladies just to be able to physically intimidate people.
Therefore, I think the best solution, game mechanics wise, is to allow Strength for Intimidation checks. It allows the Warrior archetype to pull off intimidation which suits that niche.
Of course, if your DM rules that you can get what you want even without Intimidation then I'm okay with keeping it as Charisma.
If Intimidation is the alternative you choose when you don't want to act like a complete psychopath and perform feats of extreme torture, then okay, let Intimidation be a Charisma thing, and you can also get what you want by calmly explaining to the captive you're going to cut them into very thin slices very slowly until they talk.
So I guess I'm saying that I see Intimidation as the "social" skill you use so you don't have to resort to despicable acts of physical brutality. And since you shouldn't need to be a ladies man or a bard or a politician in order to pull that off if you're a mountainous murder machine, I allow either Strength or Charisma, player's choice.
Not having to bring torture into the game, and having warriors be competent in making defeated people spill their guts (metaphorically speaking) just pragmatically makes it a better game.