I suppose that would be one the costs of renouncing. Drastically limiting the nations of the world that you could visit.
Discussion
Basically, yes. And once you have family, that calculation gets even more complicated.
The problem, mostly, is just with the information you give Uncle Sam. I haven't seen much analysis about people's "declaring" of bitcoin assets if they never sell with their taxes, but that'd be a worthy issue for any Bitcoin podcaster to cover.