So, what happens then in an area that gentrifies, like The Mission is doing currently? Demand surges and the richer kids want to move in. 75% of the units stay locked up in rent controlled tenants that represent the long-term demographic. The other units are even more expensive that if there was no rent control. It seems to me the result is great stratification of the groups. Rather than everyone roughly paying the same, you have newer, richer, and the locked in old group.
What if you didn't have rent control? Rents all over the neighborhood would shoot up and the families that have been here for years would have to move, out to less desirable areas farther away, mom & pop stores would shut down, people would have to commute, etc. So, that sort of sucks.
Compare what happens to owners & renters when an area gentrifies - the owners hit the jackpot, they get to stay there and profit from it enormously; renters without rent control are screwed, their rent shoots up and they have to move, which can be very hard on a poor family, uprooting from schools, jobs, local contacts, etc.
It seems to me that there could be some sort of compromise. For one thing it shouldn't be so easy for land lords to kick you out and raise the rent. Perhaps they should have to give you 1 year notice, or make the max annual rent raise = inflation + 5% or something. Another option is that rent control could only apply to a portion of the units, or to low income renters. If your income qualifies as "low income" then landlord can't raise rent over 25% of your income or something like that. Of course this would make landloards loathe to rent to low income people so there would have to be better laws in place to prevent discrimination.