> Are public schools better than private schools?
Yes, they are far better than private school, for those who can't afford private schools.
> Is the US postal system better than FedEx?
Yes, it's far better than FedEx for those who live in place FedEx wouldn't and couldn't operate profitably because the postal system's aim isn't efficiency, it's coverage to "everyone" everywhere, something no market solution will offer because that's not a profitable mission.
So it sounds to me like you don't understand the purpose of government and don't understand why government is necessary in such situations, because you can't think outside of your own self and realize that markets don't serve everyone.