According to an interview with Brian Henson, the director, when he reached out to Michael Caine for the role, Caine responded, "I'm going to play this movie like I'm working with the Royal Shakespeare Company. I will never wink, I will never do anything Muppety. I am going to play Scrooge as if it is an utterly dramatic role and there are no puppets around me."
Which was absolutely the right call. If I can borrow a line from Jay Bauman, Ebenezer Scrooge does not sanction this buffoonery. In his eyes (at the beginning of the story at least) hanging decorations and singing and playing and such make everyone looks ridiculous to him.
The whole goddamn story is about Scrooge being a man who takes himself too goddamn seriously.