Universal healthcare works just fine in Europe without major issues like that. It's the American political system that is broken. Your de facto two-party political system lets idiots take total control way too easily, as we can see with current US administration.

My country has universal public healthcare, and nobody forces you, or even your children to get vaccinated, monitors what you eat, or any other form of control that you're worried of. Organ donations are voluntary too, you can opt-out easily. And if you think the system sucks, nothing prevents you from taking extra insurance and using whatever private healthcare provider you want.