Density and rent are definitely correlated, but I think the causation mostly works the other way: in areas with high value (high rent), people will build more densely to take advantage of the high-value location.
That's how density increases naturally due to market forces, but we are talking about enacting policy to directly spur increased density and what its effects will be.
I would expect the policy to create lots of value, but because of the way land ownership works, I would expect most, all, or more than all of that created value to accrue to the people who own the correct land. More importantly, I would expect it to bleed away from those who don't. Shops away from Main St would be screwed, while the new lovely walkable storefronts would have $5 coffee and $15 sandwiches and the apartments within walking distance would have $5000/mo rent. Those massive flows of money wouldn't go to shop owners or workers or maintaining the infrastructure (see: NY, SF), the money would go into the pocket of whoever owned the land, because our policy choices would have just gone towards ensuring that owning the correct land was all that mattered.
It just seems crazy to me how eager people are to build an economic steamroller and then throw themselves in front of it. Fight to commoditize your complement, don't fight to help your complement commoditize you!
