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.