Who are they responsible to? 'Responsible' means 'liable to be called to account'. Who is going to call them to account if their kids get a bad education? There's a lot of bad education going on, but no one seems to be grabbing bad parents, or bad teachers, by the lapels and demanding that they provide a good education. Society demands that parents send their kids to school, and may put them in prison if their kids don't turn up. But if that school provides a bad education, and the parents know its bad, there's nothing that makes them responsible for providing a good education. They might grumble a bit, but most will not bother to seek change. I guess the kids could try and make them responsible, Kid: "Schools useless! Send me to a better one!" Dad: "Shaddup, I'm watching the football..."
Good point... keep the libraries and museums well provisioned, and well stocked, and give kids free access, then at least some kids can educate themselves. But what if they are bad learners? What if they need help?
Well there may be many answer regarding this but for me parents are only to determine this when they have seen and learned that what their child actually interested in. They should determine it by discussing it with the career consultant and after its advice they should do it. There shouldn't be any main stream education but interest and future preferences should be checked out while doing this.