How are price controls negative in markets where there are already shortages?

My question mainly concerns housing. It is my understanding that, generally speaking, rent control and price ceilings will lead to a shortage in supply. But, rent control is typically proposed in a market where there is already a massive shortage in supply. Yes, a price ceiling will lower the price below the equilibrium, but how is this a negative if there are already shortages? To me, it would seem like the only difference would be between how the product is allocated.