Consular access if arrested in a foreign country, I guess. A US embassy will try to make sure you have access to a lawyer and medical treatment, they're actually useful that way.
(Unlike, for example, Australia).
Of course, the downside is nonresident taxation. Like Eritrea and North Korea, the USA will keep taxing you even if you leave the country if you keep your US citizenship. And if you want to give up your US citizenship, there are exit taxes!