Mandatory tutoring seems unrealistic and probably wouldn't yield quality, but I do think that some kind of scaled tutoring "norm" would be incredibly valuable to society. Just as Khan Academy has revolutionised explanations of complex topics (resolving the ambiguities from school), scaled tutoring in which everyone participates could augment traditional teaching with soft skills, conversation, expansive exploration of worldly topics, and specific technical help.
Imagine a norm where ~everyone, in some way, relays knowledge and experience to youth, freeing youth from the segregation of school. It's always been odd to me that we separate ourselves (especially in western culture) from people of a different age. There's not as much integration between children and adults (outside of formalised schooling) as there could be. This separation seems to limit the transfer of knowledge but also the transfer of culture. And I think it also prevents bridges of commonality and empathy from forming, further entrenching homogeneity and aversion to difference.
It's worth asking ourselves: what would a society look like if we ~all engaged in the education of our young?