"Almost always" is way, way too broad. Yes, some parents' values are crackpot nonsense, but many are not. One does not have to be a crackpot to prefer homeschooling to US public schools.
Also, the values that the people who set up the US public school system explicitly said that system would indoctrinate children into are nothing to write home about either.
> Have some humility
Take your own advice. If anyone is being way overconfident here, it's you.
> let the kids figure out what they think for themselves
It seems to me that homeschooling is far more likely to let kids do this than public schools are.
> The public school gives them a reasonably neutral basis to do that
In the US? You must be joking. Public schools in the US are anything but neutral.