Well first I don't think non-Americans should be covered either- although really- we are paying for them anyway- if they are sick or hurt they go to the hospital and if they can't pay their bill it's just is passed on to everybody else- so we are already paying for them! And this is true for everyone without insurance- their cost is just passed on to everyone else. And because everyone is treated now- universal HC wouldn't create shortages- it just reduce costs- by eliminating the overhead of our inefficient for-profit insurance system. This would be good for everyone!
As for "do we REALLY want to have our govt telling us what we are and are not permitted to do health-wise?"- what do you think the insurance companies are doing now? They decide which doctors you can go to and which medical procedures they will cover. They are probably more strict then the government would be because they are out to squeeze every dime of profit by paying as little as possible for your treatment.