Not everyone can afford to send their children to private schools and not everyone can home school their children. I certainly would not have been able to when my kids were school age.
I find that unbelievable. However, the way you phrased it, if there's one in 10,000 who cannot do either of the two, you are technically correct.
That said, there are more than two alternatives -- a parent needs merely to explore the matter thoroughly, and options will be found. There are affordable private schools; affordable parochial schools; scholarships; tuition assistance programs; and other things that people can cut from their budget, things of less importance than their children's minds and futures.
If I could not homeschool, I would sooner apply for food stamps, medical assistance or private charity, than entrust my child to the government and its educational system.
It's hard to imagine any conservative who is intellectually or financially incapable of homeschooling. They merely haven't given it sufficient consideration.
But again, there could be 1 in 10,000!
I grew up in a neighborhood that was 50% Christians and 50% Jews in the 1950s.
My point is, the Jewish families had to educate their children at home about the ways in which they differed from the predominant Christian society, and they sent their kids to Hebrew school in the afternoons and to religious education on Sundays, when the Christian kids were also in Sunday school. Although most of the families preached against interfaith dating, we all got along pretty well and many of the friendships have lasted a lifetime, because the kids loved each other first from the age of 5 (kindergarten), and only later learned the ropes of their religious belief system.
There was a lot of prejudice and suspicion among the adults, without a doubt; and Jews were still treated unequally in employment and in some aspects of society then; many of them, especially those who served in WWII, still were very aware of the Nazi atrocities uncovered just 5 years earlier and were grateful for America; others blamed Christians reflexively and formed the backbone of the ACLU and the American Left. Today American Jews are about 90% secular liberals. Many have helped power the pendulum-swing away from public expressions of Christianity, such as the daily recitation of the Lord's Prayer in schools that we experienced. But sadly, most American Jews have abandoned their religion; whereas American evangelical Christians have become the best friends and supporters of Israel because of their belief in Biblical prophecy. Social change takes a long, long time, containing surprising twists and turns; and we must not abandon the fight.
Conservatives must operate with faith in the future, even if we must do it from underground and behind the scenes, to help the pendulum swing back again. The Bible has predicted that groups would war with one another even within families and communities: "I come not to bring peace, but the sword." The only thing we can do is equip our children privately with spiritual weapons so that they "can put on the whole armor of God" in the battle "against principalities and powers" for their souls.