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Why does it stand to reason that just because someone can afford to spend $500k on a home, they can automatically afford to spend ~$18k/year per child for private school?
Because a $500k house is a luxury. That same house can be purchased for $200k or less in Katy/Cypress etc. with no additional costs for school and only minimal additional transportation costs. The owner of the $500k house has decided that the quality of life improvements from living closer to town are worth the $300k cost difference and possibly having to pay for private school. If they can't afford the house plus tuition and their child's education is a priority, they will move to the suburbs and will no longer own a $500k house and will not be covered by the quotation. They can definitely afford to do that. If you can afford a $500k house, you can also afford to rent an apartment and pay the tuition (again, no longer covered by the quotation). Lots of options available.
While your comparison of a $200K home in Katy vs. a $500K home in the city is a little off (take a look at what $200K gets you in any decent part of Katy anymore), I agree with the rest of your point.
My line of thinking (which appears to be similar to yours) isn't that a family buying a $500K home can automatically afford private school tuition costs for one or more children. It's that they aren't typically going to be the type of resident that will be comfortable sending their children to a school that's comprised of 60-90% economically disadvantaged students. Most of them will either have a plan in place to do private school, are hoping to magnet into a better school or will move when the time comes to make that decision. I'm sure they are also hoping that the schools do improve to the point that they could consider sending the kiddos there, but it's a fallback plan most of the time.
