Seems like a free market issue, any profit resulting from development is a free market issue. Your profit margins mean worse quality housing for people, and we can see what actual public housing programs look like with Singapore and Vienna where rents can typically cost less than 20% of median salaries:

https://www.youtube.com/watch?v=LVuCZMLeWko

As renown corporate welfare recipient Bezos would say: "your margin is [our] opportunity."

If the only thing stopping development is that rich developers want to make more money, then maybe we should get rid of the rich developers and let the public decide what to build. It couldn't be worse and it'd be 20-60% cheaper too.

> actual public housing programs look like with Singapore and Vienna where rents can typically cost less than 20% of median salaries

It could work, but both Singapore and Austria have less than 10 million people amd have a residency system where you just can't come in from the outside and get your subsidized housing in Vienna or Singapore. Singapore doesn't extend subsidized housing to its foreign residents, even permanent residents, and they make up 40% of the population!

Vienna is a bit better, as it applies it to all EU citizens who are resident in Austria, but you have to have lived at the same address there for 2 years, you just can't come in and claim one.