That makes it sound like the increase was due to some inexorable natural force. California's per capita budget is over twice Arizona's, and they're running a huge deficit on top of that. If taxes are too high, cut taxes. If that means you need to cut spending, cut spending. But don't play "hey, let's tax the other guy!" games and expect that to work.
Prop13 was a big tax cut. The people behind it were minimal government conservative libertarians.
And the state did slash spending in the years following. In particular funding for the university system was hit very hard.
A lot of this also comes down to prohibiting growth. In Seattle, every time we build a new building, everyone else's property tax payments decrease. High growth years lead to lower bills. The same would work in California, they just don't build much of anything because they've made it nearly impossible to.