The money saved is in police time, emergency health care, etc. so you'd need a way for a private enterprise to claim the savings that result from housing the homeless to make this market work.

In a large city these are all city services, which implies that a startup could work with the city as the customer.

It's already being demonstrated in Utah. Giving the homeless an apartment and a case worker is not only more humane and the right thing to do, it's also a lot cheaper than leaving them alone (and then treating them when they show up in the ER, etc).

The intersection of Good/Needed Ideas and Ideas That Turn a Profit is slim.

yes, this is the grim reality