Agreed, for all intents and purposes, home schooling is about the only way that remains for children to get a legitimate education. Aside from this, there is the other option you hinted at; taking time each day after the child comes home from school, find out what they were "taught" that day, then set about deprogramming them AND THEN getting on with teaching them the right things...but over the long haul, this will be tedious and it will tend to really confuse the child - "being pulled in 2, opposite directions", especially the younger they are.
The reality has become, Home schooling may not be all that practical for many people / families to pull off... in fact, the government / system is banking on this fact, for no other reason than the fact that the system has, over the years, rigged the system to make it quite difficult for parents to even get into the position to home school their children in the first place. How many household are not in the position where both parents need to be gone at leats 8 hours a day 5 days a week just to help keep roof over head, clothes on back, and nutrition in stomachs? These hooks really got embedded in ernest when it became the neo cultural phenom of post WWII era that beckoned for both parents to leave their homes, on a regular (8-5, M-F) basis, in favor of the "workplace", but that was just the start.
Word to the wise for anyone who is considering home schooling: Avoid Government "grants" like the plague. "grants" are one of the primary tools that the system uses to subvert the interests of the people. As it applies to education, it is expressly because the government has set itself up to be an authority to "grant" funds for public education that they have been so successful in undermining public education. Any time and every time the government "gives" money to somebody - a person, a community, a county, a state, a nation, there is always the matter of implied (often unspoken, often deceptive) "reciprocity" to consider. In other words, the U.S.G., at all levels, never ever gives out money just because they are nice guys.....never gives out money without their being a well-designed agenda (hook) hidden in the $$. The basic scheme is - accept grants from your government, expect to give up something in return... and the thing you give up may not outwardly be what you see or expect it to be.
On the home schooling front, the U.S.G. - at all levels, has taken to extending it's granting arm to that level as well. Guess what? If you are a family home schooling your children, and you accept pretty much any form of "assistance"...."funds"...."grants" (and many other deceptive names for the same basic hook), whether you know this or not, this acceptance is your way of saying "thank you U.S.G. for your generosity, you now have my unspoken consent to subvert my home schooling efforts". $$$ are the main hooks U.S.G. uses to lure people towards ultimately infiltratring & undermining the wishes of the people, and this applies across all institutions, be it education, religion, healthcare or other. Do_not_take_the_money. Once you do, the U.S.G. assumes the right to dictate. As it pertains to education, they assume the right to dictate curriculum, whether it be public ed, private, or home schooling. Know this. Understand this. Do not ever forget this.