Unfortunately, when it comes to "state-run" institutions and policies, you're arguing against an ideal, rather than an implementation. I.e. You could argue it is some form of the no true Scotsman fallacy.

Additionally, there is a very prevalent and saturated belief in the current society that views anything with 'for profit' motives as somehow bad/greedy. Consequently, everything that is "non-profit" (including the state) regularly gets undeserved moral brownie points.

Public universities, public schools in "better" neighborhoods and public schools in other countries operate well. I think the commonality likely has to do with how devoted the constituents are.