What if the low tax country had low tax because it had low government spending on benefits, etc. You'd still have to pay US tax rates for little benefit.
You would still have the us foreign exclusion, at least. But most of the low tax places are not places I'd want to live (which is sad, as a libertarian); I've lived in several of them. Hong Kong is the sole exception, and there the benefits (at least roads, security, etc) are superior to the USA, due to high density and efficiency and a long period of good governance.
(also, most of the benefits of living in a high tax high service economy are not really delivered by the US government now, even given moderately high taxes. Defense spending is not particularly improving my quality of life, and to the extent it does, it is a global value which taxpayers in Japan benefit from as well. I'm not sure why the US Government and California are relatively less efficient at delivering worthwhile services than other governments around the world.)