But giving up US citizenship will cost you $2,500 last time I saw.
In theory the US has tax treaties with many other countries so you can claim a foreign tax credit against your US tax bill but it means filing more forms and more proof. You can file the foreign earned income exclusion but that effectively lets your foreign earned income push you into a higher tax bracket while then saving you the tax you would have paid in the lowest tax bracket (I can only assume that was changed because someone figured it would raise a few bucks from foreign workers, even relatively low paid workers, who weren't inclined to pay a US tax specialist in their native country to figure out how else they might avoid it)
I really like the idea of taxes being low, simple, and difficult to avoid. If they are low there's less incentive to avoid them, if they are simple you don't end up with situations where the cost of compliance is enormous to the point otherwise honest people are tempted to simply not declare something rather than spend three days reading forms and instructions, and you also avoid tax loss due to people genuinely not understanding that Form 1234, section A, part II, subsection (c)(iii)(5) applies to them because they lost the will to live six sections ago and just wrote 0 in the box. And if they are hard to avoid the advantages are obvious.
For example instead of funding roads from general taxation, perhaps they could be funded from taxation on motor fuels, taxes on servicing etc, and that portion of general taxation eliminated. I'm pulling numbers from the air here but theoretically speaking if the general tax rate dropped a couple of percent and the price of gas went up 20 cents a gallon to replace it (and maybe a 5% tax on motor servicing also created), those who use the roads the most would pay the most and it would be much harder to avoid than merely underdeclaring income or being a little creative with expense accounts.