Except schools as they exist today aren't libertarian at all. They're antithetical to libertarianism.
Libertarianism professes the extreme and utmost ownership of one's own progeny until they are acknowledged by their parents as being of majority; not deemed so by an arbitrary count of years and interference by a State power. No other person may intrude on your standards of raising and educating your children, nor free them from your prescribed regimen.
Hell, even the existence of libraries is antithetical to libertarian doctrine if you boil it down.
Just read what you wrote. Libertarianism has some good explanatory power for some stuff and offers some better ways of doing some things but doesn't scale up to a functioning civilization. It's a utopian pipe dream that has a faulty view of humanity. You end up with degenerates bringing their children to watch male perverts pretending they're women pole dancing while dressed like demons. You end up with the most broken in society drugged out of their minds living on the streets. You end up with faceless, rapacious global corporations manipulating all of society to enrich those running and financing the companies to the detriment of society, you end up with the total collapse of family and cultural institutions all in the name of Muh Freedom!
This isn't all on libertarianism but libertarianism does nothing to halt the collapse and actually empowers it in the name of individual freedom. Individuals have actually become powerless in the face of the onslaught of phony liberty. Real freedom has been lost and exchanged for licentiousness.
Learn to code
Build your own institutions
You be you
Do your own thing
Let your freak flag fly
Love is love
Just be nice
There are dozens of supposed pro personal liberty pat answers that stopped good people from slowing the descent into chaos. The manipulators in society used the opium of phony personal freedom while enslaving the country in some dystopian system of global economic slavery. You will own nothing and eat the bugs.
Libertarianism has greatly contributed to the atomization of the people and leaves us looking around at the wreckage the wolves have left in their wake wondering wth happened?
All in the name of fweedom!
Libertarianism has some good explanatory power in some limited domains but ultimately over promises and under delivers. Coming next "It's never really been tried by the right people!" Oh wait... isn't that what the commies always say?
We're not economic units and as the saying goes, no man is an island. Consumerism isn't a healthy replacement for a culture that pursues the transcendent virtuous, true and beautiful.