The tax thing is not something to be underestimated. If you want to keep an American citizenship you have to pay income tax on all the money you make living abroad at the same rate as if you made the money in the US. The doubled tax burden makes it very expensive to legally live abroad without giving up your US citizenship (which many people want to keep for a large number of reasons).
The tax code allows for deducting the income taxed by a foreign country from your US tax obligations but as I understand it's complicated, only certain types of income can be excluded, there are caps on how much income can be ignored, etc. Basically everything from retirement savings to starting a company or changing jobs becomes a big hassle that you definitely need a specialist stateside accountant to help you with.
The US is almost unique in this regard: only Eritrea and North Korea also have similar laws. Most places will only tax money you make when you live in that country.