The fraud, abuse and waste within the Medicare system is legendary, and expanding that coverage to all Americans would destroy our economy in no time.
It is true that there is some fraud. But there is a redress system. It is investigated and people routinely go to jail. In the private system, there is very little redress. It is much more difficult to detect and correct.
The reality is that every other country out there has found ways to deal with the fraud and abuse in the single-payer systems they host. And regardless, even given that, it is a far smaller number than the waste and mal-investment that comes from the overhead of the private insurance system.