The problem with line of thinking is that it assumes that Michael Caine wasn't trying to be funny. He absolutely was. It's just that the funniest thing he could have done is to play it straight.
The movie would be less funny if he was being a jokester! He's playing the straight man for all the Muppets. All of them.
And that's the funniest thing he could have done. And he could do it because he IS that actor, who could do it for real and it'd be very serious and people would clap and say it's the best since blah blah blah.
But doing that, being Sir Serious Dramatic Actor in a room full of Muppets? Hilarious.