You wrote:
“I don’t know about y’all, but my yearly property taxes (which are on the high side for where I live) wouldn’t cover the tuition for even one child in a good (or even mediocre) private school in this area...”
Maybe, but it would just be you paying for it just as you aren’t the only one paying for it now. In my area, the total cost (and I think this is an underestimate) for a public school education is something like $9,000 a year. A Catholic high school in the area announced that it will be doing it for only $6,100 next year. The parents at that Catholic school pay less than $3,000 tuition as well. The parishes kick in the rest. These are good schools too. Private schools can be much cheaper than public schools.
In my area, the total cost for a public school education is about $8500-8600 per year.
The tuition at the Catholic high school, which also gets parish & alumni donations, is $9220-9900 per year - but it's a very good school.
Private schools can be much cheaper than public schools, but usually that's because the private schools are subsidized by a church or other organization, and/or because they don't offer the same services as a public school.
For example, the tuition cost at your private school is not the actual cost per student, but you're comparing it to the actual cost per student at the public schools.
Note also that many private schools don't have cafeterias, bus service, libraries, etc., and private schools aren't required to accept students with disabilities (some of whom require very expensive services from the public schools).