Maybe part of the problem is not so much public/private, but our political system is too screwed up to really do much of anything.
Look at the cable industry or Internet service which the the US invented (Internet), but we now have one of the slowest services in the world at a higher cost due to monopolies and the industry carving it out this way/that way.
Look at schools, health care in a lot of the other countries and the US is lacking and far behind…
Public employees aren’t of a higher standard, just more politically connected, lawyer-ed and special interests (unions) to improve upon or fix.
