> 0. The creation of a deep, long-lasting relationship between tutor and tutee
I have spent over a decade in school and this has literally never happened to me. I went to second rate middle/high schools, so maybe teachers in "good" schools have some deep insight which makes interactions with them actually desirable?
In any way, this desperately does not scale, at the current ratios you would require a single teacher having "deep, long-lasting" relationships with ~hundred students at once, which just isn't feasible.
Even if every adult in the society got involved, the proportion drops by just about an order of magnitude. I can't imagine myself tutoring a single child, let alone ten of them!