Agreed in principle.
But you don't take it quite far enough.
You also need to look at the mills churning out "professional educators." If you have faulty machinery in a factory, you will turn out defective product, no matter who owns the factory or what templates are used to machine the product. The same schools that produce public school teachers and public school textbook authors/editors are the same schools that produce private school teachers and private school textbook authors/editors.
One other point:
As somebody who saw a child through 13 years of Catholic education, trust me: I had to watch what my kid was taught...just like a hawk. I can't count the number of hours I had to spend un-teaching and correcting the out-and-out error that my child was taught throughout her school career.
Sadly, too many parents (of either public or private school children...I know this from experience) don't take an active role in their kids' education and count on the teachers to teach their kids right. I shudder to think how messed up some of these kids get as a result (from teaching CCD -- the Catholic version of "Sunday School" -- I see the results of that neglect on a weekly basis)
Even in conservative TX the public schools have their share of leftie teachers. My kids would come home and share the crazy things some of their educators taught and we would discuss. Fortunately, they were educated at HOME to speak up and they did. All three of them challenged those teachers with FACTS/INFO they learned at HOME.
Parents have far more influence if one starts educating at the beginning of their little lives and like you said, watch like a hawk.