That would be an excellent idea if citizenship can be claimed and renounced just as easily as residence in one of 57 states - with a couple of utility bills.
As it stands, gaining a citizenship is pretty much a lifetime affair. However people live in neighboring countries, have families, marry, divorce and marry again, move around, get jobs here and there. They shouldn't be artificially separated by an invisible wall as long as they qualified to be citizens of both countries.
The USA shouldn't look into pockets of people who live in a different country. That would get rid of the problems, and it would be also fair and moral. There is a reason why all other countries have "close ties" conditions in their laws; if you don't satisfy those conditions you are not subject to taxation.
None of that is surprising, though. As the USA continues to sink in the sea of debt the government will be imposing more and more taxes on remaining productive workers... until none are left. These taxes will become confiscatory at some point. The economy will be driven underground, with cash-only, unreported transactions. That's what is happening in Greece right now.
As a historical matter, U.S. citizenship could be forfeited upon the undertaking of various acts, including naturalization in a foreign state or service in foreign armed forces. In addition, before 1967 it was possible to lose the citizenship due to voting in foreign elections. However, the Supreme Court ruled unconstitutional the provisions of Section 349(a) which provided for loss of nationality by voting in a foreign election in the case Afroyim v. Rusk, 387 U.S. 253,[32] . 8 U.S.C. § 1481 specifically outlines how loss of nationality may occur, which predominantly involves willful acts over the age of 18 with the intention of relinquishing United States nationality. U.S. Supreme Court decisions beginning with Afroyim v. Rusk constitutionally limited the government's capacity to terminate citizenship to those cases in which an individual engaged in conduct with an intention of abandoning their citizenship.
so it seems that at one time, the United States had a somewhat different view. Of course, I'm not an expert, and I could well be misinterpreting this.