It does work for those renting. Whether those are who it needs to work for gets greatly distorted as time goes by. The cost is also not widely distributed, but can fall heavily on the property owner.
I know just one anecdotal example and I am sure there are many other examples on the other side where rent control helps. But to me, it looks like rent control really distorts the market way too much to be an effective solution to the housing crisis.
Decommodify housing. Full stop, no rents. Housing by need.
I've lived, though as a child, in a place where housing was distributed "by need" -- the USSR, though even then in the 80s things were liberalizing some. It was, in retrospect, a horrible combination of corruption, underinvestment in housing, and what would in the modern West be considered terrible living conditions.