I just don't think the numbers hold that second homes and short-term renting account for the problem. Remember, California needs to build four million new homes just to deal with existing demand. https://en.wikipedia.org/wiki/California_housing_shortage
I'm not sure why people are so resistant to the obvious solution, but it seems to me no matter how you look at it, you just end up coming back to the most effective thing to do is going to be to get more housing built.