Personal bias attestation: We've previously homeschooled, and now my DC has returned to a flexible private school.
Warning! Screed ahead!
IMO, there are three key considerations associated with homeschooling and its oversight that become muddled:
1 - Homeschooling is the right of the child, not of the parent. It is intended to exist as a means to optimize the educational opportunity and human potential of the student.
2 - A quality education requires intentionality of design, expertise, and knowledge of the specific child.
3 - Schools serve multiple functions for children, not simply academic education. They are a critical nexus for health, social, and educational services for at-risk children. For many, they provide necessities of life and are the only stable base the children know.
As to point 1...
Homeschooling doesn't exist to support parental rights to freedom of expression or freedom of religion, although many groups have interpreted homeschooling laws from this angle. These homeschoolers and taken increasingly anti-educational positions to further entrench a damaging, extreme form of libertarianism that only really forwards the agenda of the parent, at the expense of the child.
For fundamentalist homeschoolers, it's not so much a view of "I'm for freedom of education" so much as "I'm against THAT value system and reject any association with it." The children become an objectified extension of the parent's identity, not individuals with their own inalienable rights who ought to be recipients of an individually-appropriate education.
Point 2...
As with any mix of educational strategies, the core of any educational plan needs to be advancing individual skill, be it academic, social, artistic, athletic.
This requires a level of judgment, intelligence, humility, and specialization. Even as a parent with multiple graduate degrees, I am painfully aware that I will be insufficient to support my child's learning as he prepares for university. He is already outstripping me in computer science, and I can't speak every language he could ever want to learn. This is just the tip of the iceberg... In future, I can imagine being more akin to a capable peer than an instructor as he develops his own specialties.
This is as it should be. If the goal of homeschooling parents is to educate the next generation, those parents do well to bring in specialists to advance the child's future beyond their own limitations. Our children ought to have the opportunity to surpass us, should they so choose.
Having tested the waters in public, private, and homeschooling settings, I feel the optimal mix for most children is some blend of in-school instruction and socialization, complemented by individualized, at-home learning in areas of strength. Education, done correctly, ignites passion that can't be contained inside the walls of a school, or the pixels of a screen. This is the type of learning we should be aiming for - boundless, exhilarating, and intrinsically motivating.
As we've all experienced, appropriate education for bright kids is a game of Newton's method, with constant pivoting to meet the child's needs. At what interval, and to what degree, can be up for debate, but appropriate fit for most studies needs to remain the core goal.
Unfortunately, administrative red tape often restricts an option to partially enroll/partially home school, and limits students' access to services and relationships that would serve them well. This is a loss for everyone in the system.
Point 3...
Political and legal realities will vary by jurisdiction, so please bear with me.
Where I live, there is a fragmented patchwork of resources between medical, educational, social, and community services for students. Often, these silos act in isolation, without a full view of the child's needs. Again, the child loses out.
IMO - and this is opinion only - the pendulum has swung too far in favour of privacy, and too far from a view to protecting those students who are most at-risk. The UN declaration of rights of the child clearly establishes all of these services as essential to the child's development, yet in most western democracies, parents still retain a unique veto capacity over systemic oversight.
These are just a few considerations...very happy to discuss solutions.