Earlier quoted context omitted.
Prop 13 has a TON to do with high housing prices, because it eliminates the downside of high housing prices: higher property taxes. Once higher property taxes are out of the picture, higher property values are purely beneficial for homeowners, which means there's every incentive to vote for anti-housing policies to enrich themselves at the expense of transplants and immigrants.
I wouldn't say it eliminates it. When you buy a property, you still pay taxes on whatever your purchase price is. Prop 13 just mediates the rate of increase, which is beneficial, but not immediately.
And again every year after that, including whatever increase your taxing authority may legally apply, usually the maximum allowed by law unless you actively fight it.
Texas has no state income tax and property taxes are (so they tell me) quite high as a result. My property tax is $7k+ each year. Not onerous because I have a full time job, but many of the retirees and landlords in my area did find it onerous enough to sell. Bad for renters because a lot of reasonably priced rental properly was lost, good for the city because a house like mine was torn down and 5-7 condos or townhomes took their place. Now the city is looking at easily 8 or 9 times the tax revenue for a single lot like mine since these new homes also appraise higher than mine.
If anything prop 13 represents one extreme and Texas the other. It would be nice if we could meet somewhere in the middle.