Well, and to just point out, Japan is included in the YMS. Obviously it has far more to do with the reciprocal agreements from countries that Britian wouldn't mind providing an opportunity to. Notice that South Africa, which likely has stronger cultural ties with the UK then the US and has more expatriates in the UK then I suspect Japan does, is not included.
Also, India, Pakistan, Palistine, Sri Lanka, Hong Kong, etc etc etc are all ex-British territories who are not part of the Commonwealth of Nations and don't participate in the YMS.
We assume there are strong ties between the US and the UK, but I think this is hold over from the Cold War era and in part the fading WWII generation. Culturally, the US has a lot more in Common with Canada and Australia then with the UK and economically probablly stronger ties with Japan. The UK outside of the EU has stronger cultural ties to South Africa, Australia, New Zealand, India, Pakistan and the Carribean before you ever get to the US and economically, I would say it would be a simliar mix.