One alternative to market urbanism that has received a decent amount of press coverage is the PHIMBY (Public Housing In My Back Yard) movement. PHIMBYs (or at least the most extreme PHIMBYs) believe that market-rate housing fails to reduce housing costs and may even lead to gentrification and displacement. Their alternative is to build massive amounts of public housing.
On the positive side, PHIMBYism, if implemented, would increase the housing supply and lower housing costs, especially for the poor who would be served by new public housing. And because there is certainly ample consumer demand for new housing, PHIMBYism would be more responsive to consumer preferences than the zoning status quo (which privileges the interests of owners of existing homes over those of renters and would-be future homeowners).
But PHIMBYism is even more politically impossible than market urbanism.
Market urbanists just want to eliminate zoning codes that prevent new housing from being built- a heavy lift in the political environment of recent decades. But PHIMBYs want to override the same zoning codes, AND find the land for new public housing (which often will require liberal use of eminent domain by local governments), AND find the taxpayer money to build that new public housing, AND find the taxpayer money to maintain that housing forever. And to make matters worse, the old leftist remedy of raising taxes on the rich might be inadequate to fund enough housing, because the same progressives who are willing to spend more money on housing also want to spend more public money on a wide variety of other priorities, thus making it difficult to find the money for housing.