I read Cato as much as you do, I suspect, and I have read that policy analysis. Cato places the blame on ALL third party payors, public and private, for removing the purchasing decision from the consumer. It is quite indisputable that private third party payors pay more for health care than public payors. In fact, that was the express reason the healthcare industry got so upset over Hillarycare in the 90s and fought any "public option" in Obamacare in 2009 - they knew that single payer would pay them less, and there was a great hue and cry over how that would dampen innovation and patient care etc. etc.
If you are going to argue over this, you need to learn some facts, not just opinions, and the fact is that Medicare holds costs down better than any private insurer.
Now, if you are trying to argue that we ought to abolish insurance entirely, the Cato paper is relevant. But you started this out by expressly blaming Medicare and "force" for rising costs, when in fact the private un-"forced" sector pays far more for care. What argument are you trying to make?