Bingo. Public schooling wAs a good idea that doesn’t work.
I tend to be suspect of virtually any entity with the term "public" or "national" as part of the name:
Public transit
National Parks
Public Broadcasting
National Endowment for the Arts
Public option
...and that's just a smattering.
On the other hand, I still enjoy watching Jimmy Cagney in the 30's film, Public Enemy. :-)