Humans made unimaginable progress in the last 150ish years. Many of those who contribute were raised on farms or taught in third world countries. What magic system are you envisioning that could do better than what got us to the moon?
But I expect a lot of people would drop out of the system in the absence of structure.
Especially once they've been socialized through years of instruction to not be self-motivated learners. I've read about child development that most children actively want to be engaged with adult work (such as chores), but harried adults can become impatient with the best efforts of the children. This can lead to the children no longer being interested in helping, and when the tasks eventually become chores assigned to the kids they dislike doing them, and don't have the willpower to stick with doing them. I think this process would generalize to general education.
Things can be done with individualized or mentored instruction within the current system without using too many additional resources.