before the state schools schools for the poor were mostly church run. i don't want church schools personally. i don't muslim schools - if you've heard what's been going on in a few of the inspected, on the radar ones imagine what they'd become without regulation? education should not be religious indoctrination nor should it narrow and ghettoise one's intellectual landscape.
think too that without state legislated education there would be sectors of communities where female children were not educated at all, potentially not even taught english. large swathes of the population might barely come in contact with each other - racial tensions that usually ease over a couple of generations via mixing at state school would become more entrenched and possibly even encouraged and taught at religious/cultural/ghettoised schools.
without a state healthcare system how does one monitor for child abuse? no health visitors to know that a baby is being abused or a mother is suicidally depressed. that's if she hasn't died in childbirth of course because the church led health care would try to take her baby away from her because she's single so she didn't dare go to them.
and where will industry recruite from? modern industries require a high level of skills even for their most basic jobs these days - how will they source the people they need? ok the rich and privileged or the religious elite groups will manage to ensure their children are well educated but what about the rest (because those people won't want to work for peanuts in 'little' jobs that actually need doing).
you'd have ghettos - cultural, religious, economic, etc and massive unemployment and lack of a useful workforce and business would go elsewhere to countries where the state DOES educate it's population. you would have nightmare policing and security issues.
one thing you don't seem to really take on contrarian is that business profits from state education and healthcare - it needs a fit and educated workforce - the state isn't a charity but a function and society needs a healthy balance of state, private sector and people groups (3rd sector, religion if we must, unions, etc) to function.