I would love to get there, but it would be a difficult transition and it would be fought tooth and nail by most people.  

Pragmatically in the short term, I'd switch to a system that supplied anyone who wanted to homeschool something like $500-$1000/year (could be up front or reimbursement for purchases made for the student) and up to something like $5,000/year for those who wanted to send their kids to private school (I'm betting most private schools would suddenly manage providing schooling for $5,000/year).  Currently states spend $16,000 - $25,000 per student per year based on one article I checked. This would massively reduce spending while giving parents choice.   Over time, as more choices became available, fewer and fewer students would attend government schools and they would slowly be closed or combined until there were few, if any, left.  This would allow a smooth transition and allow new options to slowly come into existence.  Once most of the students leave the government schools, then they could be eliminated entirely (to reduce costs).

These amounts could be tweaked as needed (different cost of living in different states or more variability based on hybrid options or helping with some daycare) and potentially there could be a payout amount between the homeschool and private school options for hybrid schooling, where the parent does much of the education, but pays for schooling in areas the parent feels unable to teach.

It isn't perfect, but it would be much better than what we have and would give a smoother transition.