You can leave most countries and renounce citizenship, typically with some hoops to jump through but it can be done.

The questions of where you'll go and how you'll support yourself are something that you'd best figure out before starting that process, because after you start your country of origin may well say 'not OUR problem anymore' about you.

That's not really the US's fault though, right? "You're free to leave, but if you want to stay here you have to abide by our rules," sounds reasonable I think. There are countries in the world where you're not free to leave even if another country will take you, and this argument would hold a lot more water.