So, if no one wants to do it, then where does this idea come from that it's a good idea? What's wrong with allowing the market to determine what kind of housing is going to be built? I'm skeptical about this whole Soviet Russia style concept where somehow the government ought to be involved in building a bunch of crappy, cheap, high-density apartment buildings.

I'm comfortable with the idea that the market will figure out the right amount of housing, and the right price for housing. I'm not saying that there should be no zoning laws, but within whatever zoning laws you have, why not allow it to be a free market? The forces of supply and demand do a good job shaping what supply is provided. Zoning itself may be a big part of the problem as well:

"The artificial upward pressure that zoning places on house prices—primarily by functioning as a supply constraint—also may undermine the market forces that would otherwise determine how much housing to build, where to build, and what type to build, leading to a mismatch between the types of housing that households want, what they can afford, and what is available to buy or rent" ( Jason Furman, Chairman, Council of Economic Advisers)

Perhaps we'd all be better off leaving much more of land use to the market as well.

Actually, if you could build 1000 units of really high end housing in place of, say, 100 units of average, low-density housing, it would still help, because it lessens the pressure on some of the existing housing.

That's the point, to increase the supply.