Because you can't tax money in another country? lol
The US does tax its citizens even if they earn income abroad, and there is a fee you have to pay for renouncing your citizenship, so OP's idea is already being practiced to an extent. Although you could get away with not paying taxes depending on the country you move to.
Anyway, it is of my opinion that making it impossible to avoid paying some sort of money to the federal government is theft, so I don't think there should be a fee to renounce citizenship.