How does this differ from the requirements that American citizens enter and leave the US on a US passport (Boris Johnson notoriously had a problem with that)
My former MP also had a problem with that - something about needing to use his UK diplomatic passport for an official visit and the Americans not being terribly keen on that (I've probably got the details wrong, but point is, it isn't just Boris). Nothing that some seriously high powered people running around phoning each other out of hours couldn't fix, but it was still a hassle.