You are assuming that the private sector will always use that money more effectively in creating goods and services. I’ve never seen compelling proof of this, quite the contrary, there seems to be ample evidence to the contrary. The private American health care is extremely expensive and inefficient compared to almost all other public sector health care systems.
In my home country Norway, we do a lot of mixing of public and private delivery of welfare services such as child care, garbage collection or elderly care. The private sector has never consistently managed to do these services cheaper and better than the public sector. If they did, they would have one all the bidding rounds to carry out these services.
Quite the contrary many services have ended up more worse and more expensive after the private sector took over. I don’t personally have a problem with the private sector carrying out services, but I only want them to do that when they are doing a better job. Too often they seem to get the job because there is an ideological rather than pragmatic drive to privatize as many public sector tasks as possible.