Sure, it's not trivial, but it's not a startup-solves-it issue, at least over here. Even without a lot of NIMBYism, the local administration isn't getting the permits done and doesn't open up spaces. In the metropolitan area I live in, we "need" about 50k flats a year. We're getting 6-9k. The bottle neck is in the government, and unless you replace that government with a startup, you're not going to solve "the problem".

The other problems with housing are solved pretty well by coops, even though I'm thinking of moving out of mine - providing affordable housing is nice on paper, but it also gets you neighbors that are socially challenged.