There's also the political ramifications of rent control: people paying far below market rates have little incentive to support the construction of additional housing, and more frequently try to shut down developments. One of the most ardent anti-development activists in San Francisco turned out to be paying $740 a month in an apartment estimated to rent for $4,500 at market rate. Get rid of price controls, and I bet this person would stop being a NIMBY overnight.
> That being said there is no rational reason to support advancing rents past wages. Why would there be?
To spur the construction of new housing! If there's a food shortage, the last thing you want to do is cap the price of bread. No, you let the prices rise so that more farmers grow food. If people are struggling to buy food maybe subsidize it to make it affordable. If the price of food is capped, then there's nothing to drive greater food production.
The same dynamic exists with rent control: cap the price of housing and people end up paying less than market rate. Developers realize they won't be making a favorable return on investment when they build in a rent controlled city so they move elsewhere.
Now, there is a solid argument that apartments have gotten too expensive due to regulation. Look at any apartment building and what do you often see? Its cladded in tiny 3 feet by 8 feet balconies that can scarcely hold a cafe table, it often has some big central mostly useless courtyard like area within the complex itself to check a box for some outdoor space requirement, and it has a parking garage that extends 100 feet into the earth. All of these things are also brought on by regulation that demands the developer to build these things if they are to see the build approved. These can also all be nixed, and in many cases they have been used pretty much to just serve as a vehicle for graft for city officials. Put a bag of popcorn in your microwave and then read about Jose Huizar if you want a brief of how these sorts of things function in large american cities.
That being said there is no rational reason to support advancing rents past wages. Why would there be? Its the snake eating itself; the race to the bottom is that you end up with only the high income sliver of your regional economy of workers living where the job activity takes place, which is pretty wholly terrible for the environment and also deprives most of the opportunities that present themselves from being able to live near a major job center. We should be doing anything we can to prevent this race to the bottom, just for our own climates sake if the mere wellbeing of your fellow worker isn't enough.