There was a time in the 90's when "school choice" was a hot topic among the conservatives. The parents of public school kids wanted vouchers in the amount of the cost to educate a child in Texas (@ $5000/year) to pay for a private school education, i.e., a better education. However, on the private school side, the private school principals wanted to remain "private," not accepting public monies of any kind, for the reasons Oh so artfully stated above.
The conservative GOP legislators were so ga-ga about vouchers they extended the opportunity to us homeschoolers as a thank you for getting them elected (don't ever forget who the grassroots GOP consists of). We also politely spat in our uneducated lawmakers' faces. Our only mantra still remains to this day: "just leave us alone."