Times have changed, housework-wise. When I was a child, I used to help my my great-aunt do laundry with an electric wash tub, a hand mangle, and a hand rinse tub. Then hang the clothes on the line! And that was an improvement from the days when her washer was diesel-powered :-).
I understand your point, and of course the government can force the citizens to send their children to public school, irrespective of the parents' preference. However, the government cannot force people to have children. It will be interesting to see whether bribing them will work.
Diesel powered washers wow. I can remember that my mom did clothes in a tub with a wringer and all until I was about ten or so. Heaven help you if you ran into the clothes line and knocked clothes off.
There are several things about homeschooling that I am skeptical about: one is that I do not believe most parents are qualified to do it, have time to do it right, would teach with the proper degree of objectivity (even with the Leftist dominated teachers' Unions there are still different perspectives simply because people just don't agree about everything), and it is unlikely that proper scientific equipment is available for teaching science.
I understand people wishing to remove their children from pernicious influences but one should not assume that kids believe much of what they are taught. I do not believe the state should completely restrict homeschooling but I also do not believe it should allow anything to be passed as schooling. My late wife was a teacher who anyone would have loved having she loved her kids and they loved her. The kids she taught would almost entirely have been totally lost with homeschooling given the Welfare Class nature of the parents.