Note that about half of the insured are insured through US govt programs. Interestingly enough, the cost of those govt programs is about the same as the cost of the private programs that cover the other half of the insured. And, the results of those govt programs is not better.
If you're going to argue that the US govt can do better than the private sector, you should explain why it doesn't. Same cost, same results. Why will making it universal change any of that?
Better yet - work on the US govt programs and then open them up at cost. When they're better and cheaper, folks will flee the private system. Until then, why should we believe that they will be any better than they are?