Crotchety isn't the issue. There's nothing that says a young actor can't be snarky, sarcastic or grouchy, after all. The problem I have is that The Doctor is a very old being, with a ton of experience and a lot of baggage. That should show in their bearing, their attitude and to a degree in their face. So some fresh-faced youngster, while they can, as Tennant did, portray the characters' intelligence and knowledge perfectly, can't always capture that depth of experience.