A lot of property taxes go to funding schools, so...more housing = more kids = more money need to educate them. It is nice that they use property taxes from businesses as well, but to completely detach the education need formulas from tax formulas sounds really dangerous.
Are any school districts outside of Prop 13 California funded by primarily income or sales tax? But ya, you would need to do something like that if you were to tax land rather than improvements given schools, police, and lots of infrastructure needs scale up with improvements.
A significant part of the educational budget of the US comes from federal funds and federal funds are almost entirely income taxes (some other sources exist).
Most schools receive very little funding from the federal government. Maybe the poorest school districts this makes up a significant part of their funding, but for most school districts it doesn't.
The table implies funding origins via taxes (local vs. state taxes, for example). I don't think any ED money is going to CA first before going to the districts. CA is also a special case where more funding is state level (due to Prop 13).