The Doctor also regularly intimidates whole alien galactic empires and eldritch abominatios from beyond space and time. By just standing there, talking. And pointing out he's doing so without having a single weapon on him. Tennant was great at that.
“Don't play games with me. You just killed someone I liked. That is not a safe place to stand. I'm the Doctor! You're in the biggest library in the universe. Look me up.”
In games I run, mimics hate being covered in alcohol because it dissolves their sticky goo stuff, but can still be bribed with beer because it makes them feel great.
Kilgrave was indeed something else (I'd say that Tennant managed to make him significantly more intimidating than the original), but he's also absolutely terrifying as the Doctor, when he stops trying not to be. And as someone else pointed out Good Omens' Crowley can be pretty intimidating when he wants to.
Tennant is actually very good at playing intimidating characters.