I don't think USAH should care about losing Prince. If he can help grow the sport for Belarus I'm all for it. The varied citizenship practices amongst IIHF countries is a challenge, but I imagine they're not too worried about it until / if it starts affecting top players, which Prince is not. I think the IIHF is fine with it because the 'get quick citizenship and play' tactic is largely employed by smaller countries or those trying to elevate the sport. If lower tier Canadians, Americans, etc. can help Great Britain or Belarus build reputable programs, that's a boon for hockey overall.
I don't think it does anything in terms of growing the game there. Quite the opposite. Domestic players, who dream of representing their national team, get snubbed because their management decides to acquire outsiders instead of improving their own youth program.
Not only that, it hurts competing countries also. Belarus has a stronger team than Slovakia in this tournament. Imagine being a fan of Slovakia, or even Switzerland or the Czech Republic, and potentially losing to Belarus and missing the playoffs, when you know you're in fact better and you'd win if it wasn't for a few players who shouldn't be there.
As a Swede, I would never want Sweden to start acquiring american NBA players to be competitive in basketball. Nor would I want other countries at our level to go this route and beat us by such methods.