Basically, poor people, and people struggling with disabilities and disadvantages, will get far less education. Overall, society will see drastically less education as a whole. This includes not just technical education in math, physical sciences, automotive tech, etc., but also in civil society areas such as social studies and literature.
Current education systems are very far from ideal. But abandoning them for an extended period of time under the belief that people will see it as in their best interest to learn to be good citizens on their own is potentially catastrophic.
It might be true for some proportion of HN readers, but it's not clear that this generalizes. After all, those of us who self-study are often learning programming-related topics for which there is both abundant online documentation and clear, objective feedback on progress. We also tend, as a community, to have reliable access to the necessary technology, large amounts of disposable income (and security of leisure time that comes with it), a high level of prior expertise, and exposure to role models in self-learning. It's easy to take these things for granted, but they all certainly help in developing self-study habits.
As much as I might personally like to see everyone be more self-driven and self-reliant in learning, I share the concern expressed elsewhere in this thread as to what the impact of a sudden shift to remote learning would be on equitable access to education.
Incentive and opportunity is something quite different then "there is no other option".
And it also requires not just resources, but also parent that could be good teacher. And even among richer people, not every parent would be good teacher, quite a lot would sux at it.