Of course U2F devices should be excluded from the list, and there should be some warning text about "do not allow important devices on random websites", but that doesn't seem like a huge deal.
Playing devil's advocate here (because I do agree this would be ridiculous but I think this is worth pointing out), but you can never completely rule out tricking the user. They could always download a file and run it to bypass the browser or something. So the question really is how easy it is to trick the user here.
Of course U2F devices should be excluded from the list, and there should be some warning text about "do not allow important devices on random websites", but that doesn't seem like a huge deal.