That assumes rent controlled units actually benefit mostly the underprivileged. They don't.
They create a strong incentive to keep a flat indefinitely. It's not unheard of for a person to continue renting a rent frozen apartment after they buy a house because the rent is so cheap - effectively it's a second home.
There's also plenty of corruption. "Knowing a guy" is one of the best ways to get a rent controlled unit since the wait time can be years.
> "Knowing a guy" is one of the best ways to get a rent controlled unit since the wait time can be years.
That's how military housing works. There's an underground "economy" of favors.
Even if they don't benefit economically, there's some value in having them feel that they are valued and have a voice at the table. Such policies can provide the popular support needed to implement other more economically optimal policies, and we're seeing this happen for example with the mayor of New York.