There were two other comments in this same subthread pointing out that people are in fact moving out of California. (One of them has been deleted.)
It's almost as if f(california_net_migration) is multivariate.
> Less houses will be built, as less profit is being made.
Residential construction in California has been approximately steadily climbing since 2008 [1]. Even if I believed your premise -- which I don't -- reality disagrees with it. The conditions surrounding new residential construction are so much more complex than merely "omg rent control".
A San Jose Mercury News article published last year discussed some of the influences in new residential construction: https://extras.mercurynews.com/blame/
Strangely absent from that article though is that people don't want to just "live in California"; they want to live in the same places where everyone else is already living. There is plenty of affordable land in the central valley, in Kern County, and lots of other places with stagnant economies and depressing downtowns. But if you want to live in San Francisco, expect to pay a stupid amount of money for a vacant lot [2]. Again: this is not a situation that rent control is going to have any effect on whatsoever.
> Therefore, prices will be lower for those already housed, yet more people will be unable to purchase a home.
Funny, this sounds quite a bit like the situation that Proposition 13 created back in 1978 [3].
And yet, proposition 13 is rarely cited as a significant contributor to California's housing issues, especially by the "this is simple supply and demand" crowd. Personally, while I suspect proposition 13 has contributed, there are lots of other factors, including foreign investment [4].
But maybe we'll soon see just how much of an effect that particular factor has had in housing costs [5].
Sure though, rent control is gonna have a huge impact on California's housing prices. Totally.
[1]: https://journal.firsttuesday.us/the-rising-trend-in-californ...
[2]: https://sanfrancisco.cbslocal.com/2016/10/21/san-francisco-v...
[3]: https://en.wikipedia.org/wiki/1978_California_Proposition_13
[4]: https://calmatters.org/housing/2018/03/data-dig-are-foreign-...
[5]: https://www.cnbc.com/2019/07/17/foreign-purchases-of-america...