You get to the gate, your carry-on has already survived check-in, security, and the terminal walk, and then an agent says it has to be checked. A few minutes later, you find out there’s a fee attached. That feels backwards to a lot of travelers, and honestly, it’s why this question comes up so often. The short answer is that it can be allowed, but it depends on why the bag was taken from you and what the airline’s published rules say.