If the rents are high because of a lack of available units, you build more units or make more units available.
If you are at peak carrying capacity in a given city you need to expand infrastructure (vertically or horizontally) to support more & denser development.
The trick is both can require public spending to make work. You can't just rezone and let a city go and expect magic in the first case scenario. You often need government subsidized building of cheap apartments to spur the economy to build up and attract investment / higher paying residents to build generalized housing. Most developers are looking for the highest margin building they can do, and while in theory any potential profit from building should eventually be met there are only so many construction companies, especially urban highrise class builders, and they prioritize the best deal.