I think you're arguing that richer neighborhoods should have nicer schools, roads and parks. Granted, SF is an exception here, but that's precisely how things work elsewhere in California.
And if richer neighborhoods don't get that, California made annexations pretty easy, which is why you see those tiny municipalities in the vicinity of Los Angeles, San Diego, Anaheim, etc.
One can't really arbitrage that effectively.
Municipalities can't run consistent deficits, so the new schools, roads and parks will be built after a wave of newcomers buys properties, locking in higher prices and higher tax base.
In case there are no such newcomers (i.e. everybody is maximizing their Prop 13 benefit by not selling), the municipality just sticks to the last year's budget with a 2% increase permitted by Prop 13. But in that case new schools, parks and roads that make the neighborhood better don't appear either.
That's a really good reason to stop funding those things through property taxes.