I still don't understand this. Most people are motivated by a lot more than the desire to pay less rent. Jobs change, people move, they go upward in their careers, etc.
Is there any evidence to suggest that rent prices are actually "strong incentives" to not move? I think this isn't true.
I think people are much more motivated by their social circles, their job prospects, upward social mobility by working hard, or starting a business, etc. There are so many factors that go into choosing where to live that I find it difficult to believe that simple rent control like this would "strongly incentivize" people at large to not move. Especially in California.
Anecdotally, I have voluntarily left 5+ rent-controlled apartments without even a thought to them being rent controlled and my next place being unknown. It simply has not mattered, because the amount saved by rent is often far less important than the other aspects of life.