That's what Sweden thought as well. Almost all "owned" apartments in Sweden are coops, yet there is a gigantic housing crisis in Sweden.
A lot of places around the world have problems with affordable housing. In all those places attempts have been made to solve this issue. If this were an easy problem as many people seem to claim it is (I am not saying you said this) then it would have been solved already. It is not. The people running this fund realize that this problem is a lot harder than what it looks like on the surface.
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.
I agree, coops are the way to go with housing. They can be supported by the state in terms of low cost land rental or tax benefits.
I am always wondering why not more businesses are structured around coops and the state is not pushing this more.
You don't want to live in government housing when money is tight and some company offers a quick buck to pluck up that hole in the budget. Coops don't have that problem, they can't be sold, as they're owned by their members, which are largely also their renters.