Then renters can afford the larger rents, and after the dust settles all you've done is take money from one of the state's pockets and put it in another, no?

Yes. Seems like I typed before I really thought about it. :/

I guess what you'd want is to tax the hell out of rental properties, then put that money to first-time mortgage assistance.

The problem is the financialization of housing in the first place. You have to figure out a way to reverse that. Making speculation illegal probably isn't feasible, but could you require that renters earn equity offsetting some portion of rental profits?

Then you'll be subsidizing your own tax.