"Possibly unpopular opinion: school is not negotiable for children and so there's no guiding. It's pure coercion."
There are lot's of things which are non-negotiable for children. Things like brushing teeth, going to bed and washing hands after toilet. All of which have some intrinsic value beyond tradition.
Coercion is the action or practice of persuading someone to do something by using force or threats.. There are other means of guiding children to do something. These include gentle reminders, routines and and just agreement.
And, yes, coercion as well, when all other things fail. Hopefully not that much.
If a child goes routinely to school I would not call this an action under coercion, unless the child has learned e.g. that he needs to go to school so he does not turn into a destitute when he grows up.
"School was a great alternative at a time when it was the only place to get information. This is no longer true."
I don't think there ever was time when "school was the only place to get information". I would claim this is location based (if true even then). I.e. rural villages with low rate of literacy vs. a literate society with access to books.
Or, in pre-literate societies, just having access to a sufficient number of people would probably provide a venue for some information access.
Besides, providing information is not the only function a school has. My kid internalizes all math he is taught immediately and combines all new facts he learns into a logically cohesive model of the world which he has structured in his head.
However, he does need to learn how to live in a society and how to work with other people and school provides a good place for that.