I think we can find quite a few examples, though, of things that are privatized but are horribly inefficient in the US (and are done much better in other countries). Healthcare is the primary example that comes to mind.
And I'm honestly not sure where all the USPS hate comes from: I think they actually provide pretty damn great service[0], at a pretty damn great price. Their financial struggles are mainly due to Congress heaping unreasonable financial obligations on them (obligations that companies like FedEx or UPS would never have). I don't think I could say they're objectively superior to the private couriers, but they're not objectively inferior either.
You mention education, and the issues there mainly boil down to lack of funding. The US spends a pittance per student compared to countries with much better public education. You could say ok, well, that's just proof that the government can't manage education well. And I guess that's maybe not false, but consider that a big reason why education isn't funded properly in the US is because of people (like Betsey DeVos) who want to kill public education, not because they truly believe the private sector can do it better, but because doing so will enrich their cronies. Regardless, you could flip it around and say that the US's public education is amazing considering how under attack its very existence is.
> the tort system, which is partly under private control
Not sure I understand what you mean. In a civil trial, you still have the same lawyers represent you, and you get the same public-servant judges, etc. The state's word is final when a judgment is rendered.
And in fact we do know what happens in civil matters when we try to privatize it: arbitration (often binding, because god forbid we disallow that), which is hardly a paragon of fairness or equality.
> ... is far more fair than the criminal justice system that is under public control
I don't think this is an argument about public vs. private, though. Yes, in a criminal trial, the prosecution has many, many tools available to them that a plaintiff in a civil trial wouldn't have, in the form of whatever law enforcement apparatus is at hand to help gather evidence and find witness testimony (and perhaps other nefarious things that they're in a unique position to get away with). But there's really no other option; you just can't treat criminal cases in the same way you treat civil cases.
There's a ton of inequality in our judicial system, but that has nothing to do with the public-sector private-sector dichotomy. In a civil matter, the state is a mostly-disinterested party, while in a criminal matter, the state has an inherent interest.
> which is why killer cops never go to prison but their victims get million dollar damage payments
No, that's because criminal proceedings have a much higher evidentiary standard. Which is how it should be, because the result of a criminal proceeding can deprive someone of their freedom or life.
[0] Two nice things the USPS does that the private couriers don't: pick up mail and packages from my building for free, and keep a key to my condo building so I don't have to be available to let them in.