I actually think homeschooling is a benefit to kids and parents even outside of a fiat system. Nobody cares about kids more than their parents. Nobody knows the kids better than the parents. The best way to help a kid is to customize education to each particular kid's skills, weaknesses, learning style, and interests. No large system can do that, but parents can. Homeschooling also strengthens family relationships which is a major benefit.

The fiat, government indoctrination system will motivate parents to homeschool. The many benefits of homeschooling will keep those families homeschooling.