There is no choice really. The representatives are not going to turn away people from emergency rooms. Just like they are not going to stop requiring people to have auto insurance. Your original point that a person's health imposes no liability on others is incorrect.
Sure there is choice, every two to four years. You just don't want to pay for the charity your representatives have chosen on your behalf, so you force the recipients to pay.
Just because you don't have personal, immediate choice of whether or not to extend charity to a drunk with heart trouble doesn't give you any ethical or moral basis to force the drunk to do anything other than not drive a car.