Well, step 1 would be for us to stop making it illegal for developers to do exactly what you are suggesting, ie we should get rid of building height limit zoning laws.
Sounds good. How can we convince people sympathetic to the plight of the homeless that burdensome regulations actually raise costs and hurt the disadvantaged?
Ugg, you are describing the problem of the century.
Unfortunately I don't have an answer to that. It is apparently quite easy for people to convince themselves that they are "protecting the character of the neighborhood" while also hurting other people, while not realizing it.
I think that the only solution is to get together a voting cohort of renters, that will fight and vote for their own benefit.
But this is hard work and there are no easy solutions.
