The alternative of large schools (and what is being championed here) is home schooling children. Not only does that not scale, it also disproportionately favors the wealthy as families with already limited means are unlikely to be able to commit neither the money nor the time (on top of work everyday) to teach their children.
Even if you fix the scaling issues and the disproportionate income problems, you still have parents that simply don't care. When I was in school it was in vogue (in my locale) to take your kids out of public school and begin to homeschool them. But it turned out that parents' seemed to think that was the magic bullet, and their children were largely left to their own devices to figure out material, a schedule, and to somehow still be able to interact with kids their own age.
Obviously, I am not a big proponent of home schooling. I actually liked going through public school. I will forever wager my small town public school education against any home-schooled person's education any day.