Here in Ithaca NY, Collegetown used to be a sleepy neighborhood of large divided houses rented to Cornell students.
About 20 years ago they began densifying like crazy. 2-3 story houses for 8 people became 8-floor apartments and studios. And you know what? Rent is higher than ever! Everywhere!
Once you build up you can charge higher rents, which means the landlord next door can charge slightly higher rents, and so on.
Building housing almost never lowers rents for the non-rich, unless there is a massive recession (Florida), or an equivalent rise in wages. People build dense housing because they expect people to keep coming...
Evidence? In the last ten years the typical apartment in Ithaca has gone from $550/mo to $1500/mo, which seems far in excess of the extra 1,500 people or so spread across the city, especially given they've been building new apartments like crazy the entire time.
If a lot of people want to move somewhere, rents will rise with or without new housing!
So developers started building houses, which caused more people want to move there and rising rent prices? You sure you have the right cause and effect there? It sounds like 20 years ago demand for housing prices started to rise and the supply never kept up.