People like to look at rent control from a purely economic lens, but the sociopolitical aspect must also be considered. A suboptimal economic outcome might actually be optimal when all factors are considered. Social harmony and a feeling of hope for underprivileged residents are hard to value, but we must admit that they do have value.
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.