That sort of thing pretty much made Tom Baker's Doctor though. Although admittedly Tom Baker could turn it off when he needed to.

(Incidentally, since I am feeling extra pedantic tonight, do you mean "carpet chewing" or "scenery chewing"? "Carpet chewing" does come from the jokes about Hitler's peculiar rages, but the notion of "chewing the scenery" is a theatre term much older than Hitler, referring to any sort of overdone performance. While Tennant doesn't bother me as much as he evidently does you, I could see either one applying to some of his performances.)