I don't think your analysis is valid in California. Public high schools in California receive most of their funding on a per-pupil, attendance-weighted basis from the state on a redistributive basis (all property taxes from across the state are pooled and redistributed).
Parcel Taxes allow wealthy areas like Palo Alto to have much higher qualities of education. School District quality is probably one of the number one factors for families looking for a home.
Most school districts in California don't have any parcel taxes. There are definitely some like Palo Alto and other Bay Area and LA school districts that do, but they serve as a relatively small boost (0 to 20% of the district's budget). But yes, to the extent they constitute a significant portion of the revenue, the dynamics described by the parent post play a role.
Parcel taxes are known to be a poor funding mechanism for this reason, but they were the only viable way for districts to raise extra money while working around the toxic side effects of Proposition 13 (https://ed100.org/lessons/parceltax), which illustrates its long shadow in California state law. Prop 13 is of course responsible for multiple other self-reinforcing anti-growth incentive loops.
My favorite loophole on Prop13 is where a Real Estate Trust can purchase a commercial property, and then sell portions of that Real Estate Trust to LLCs. Those LLCs maintain their ownership percentage, but investors can buy/sell shares in that corp without triggering any of the Prop 13 change-of-ownership triggers, and therefore keeping a cap on their tax increases.
