Turns out the charmless brute really likes killing people.
How would you know in this situation that the big guy is a gentle giant and not a murderous giant? Not every big guy is automatically a nice guy.
Charm is necessary when the threat that you are using to intimidate isn’t real or the victim doesn’t think you’d pull through.
If you are tied to a wall and some uncharismatic weakling threatens you with a knife, the threat is very real after that guy starts punching holes in your arms.
Tbh, if a big guy pins someone to a wall and chokes them, the situation is not anymore about how intimidating the big guy is, but about whether the victim is prepared to die for the cause.
On the other hand, charisma-based intimidation makes a lot of sense in e.g. blackmail situations.
So I’d say, strength-based intimidation doesn’t require a dice-roll since it only depends on the victim.
And charisma-based intimidation only applies for situation, where the victim doesn’t know whether the threat is real.