Makes sense they'd bolt the fuck out of Japan, where they can't get married. In the US, Mitsuki can actually play rock (because in Japan it's very niche) and they can actually marry.
Mitsuki's problem is that she can't play the music she wants in Japan. Out of Japan, the problem is solved.
Wouldn't this just be going from a place with little demand and not a lot of competition to going to place with too much demand and endless amount of competition?