Americans abroad shouldn't pay taxes (since they get basically no benefits) or vote (why should those who live abroad affect the laws they are, largely, not subject to?)
Americans abroad get a very valuable guarantee though. If shit hits the fan the full force of the US Military and Government is around to help out. They also are a last resort for Americans in emergencies abroad. Emergency assistance, flights and travel back home, etc.
It's not like we give up everything but leaving the country.
And your citizenship allows you to get visas/dual citizenships that you wouldn't have access to if you weren't an American citizen. An American passport is pretty valuable, even if you don't live in America.
This is all less relevant if you move to, say, the EU, but it's still worth noting.
It's not much of a guarantee when it depends on the administration in charge. Recent debacles come to mind first, but the willingness of the government to help (in particular, with your mention of the military) is extremely variable.
It's not like we give up everything but leaving the country.