I'm not sure the opposite is true either, i.e. that expensive homes are a proxy for good schools. I've also worked in schools where the families were affluent, but the environment was toxic due to the behaviour of students and parents.
I went to school in a poor district. Pretty much all the students at my elementary school were poverty adjacent. Most of them were good kids, but that didnt really matter because the 10% who werent often ruined it for everyone else. This is a one bad apple spoils the bunch scenario, so the incentive is to make it as hard as possible for even 1 bad apple to be in the school. Of course there are plenty of bad apples among rich kids too, but as you can imagine the politics is different there.
The actual case is about whether the poor school system was allowed to have higher prop taxes than Texas allowed. In the details are the inequality argument (hence 4th amendment being at issue).
In my opinion state INCOME TAXES are the way to fund schools - lower prop taxes and make schools more equal - now everyone is happy (except those who want their 3M home to be in an exclusive school district).
Private schools, even ones that receive less tuition per student than public schools of the same district prove this point because they can set a higher bar and more readily kick out disruptive students.
Nationally, per student cost at Catholic parochial schools is roughly 1/2 of public schools. (Couldn't find California specific numbers, but it tracks what I've seen.) That's cost/spending; tuition is even less. Special education programs eat up 1/4-1/3 of public school budgets, so there's still a gap after accounting for that.
1973 was over 50 years ago. Even the poorest, most "backward" states have long ago largely remediated spending inequities. What you hear today to support claims of inequity are cherry-picked esoteric cases to drive outrage, just like every other topic today. In reality there's clearly much more going on than what advocates for this or that would ever admit.
In any event, "picking your customers" is exactly the point of the previous poster(s). Money doesn't really explain what we're seeing. Once upon a time there was a very strong correlation, and people presumed causation, but now it's quite clear that the causation wasn't there. Certainly not directly, which is why throwing more money at the schools isn't helping.
Public schools have to take children that do not want to be there and make it everyone's problem, and their classmates suffer for it. Maybe this public school policy is the issue that should concern you.
It's also a feedback loop, once you're known for "good schools" then the homes become more expensive. If you don't care about moving then it's often cheaper to buy a home to send your kid to a good public school vs. sending them to private school.