It's very funny that, again, multiple points of the article they link undercuts their suggestion that market rate housing is, in any way, a solution to the problem. It literally points the finger at market-rate developments for exacerbating the homeless problem:

>Half a century ago, America invented modern homelessness.

>The stage was set with the shuttering of psychiatric hospitals in the wake of abuse scandals and the introduction of new psychotropic medications. Then cities started offering tax incentives to owners of flop houses, or single-room-occupancy hotels, to convert their properties into market-rate rentals, condos and co-ops. In New York City alone, more than 100,000 S.R.O. units that had housed substance abusers, elderly singles, former inmates and the mentally ill were lost.

And nowhere does it imply that building more of them was the solution to Houston's problems.

>Encampments like the one in the underpass lay bare decades of calamitous decisions by planners, politicians and health and housing authorities. One in every 14 Americans experiences homelessness at some point, a population that is disproportionately Black. Eradicating homelessness would involve tackling systemic racism, reconstituting the nation’s mental health, family support and substance abuse systems, raising wages, expanding the federal housing voucher program and building millions more subsidized homes.

Or here:

>The Houston that Ms. Rausch grew up in has changed. A once-abundant inventory of affordable housing has shrunk drastically. New construction focuses overwhelmingly on the top of the market. As elsewhere, giant investment firms like Blackstone have been gobbling up housing stock, pricing out middle-class and lower-income residents. Making matters harder, eviction filings in Harris County are now soaring: they’re higher than they were before the pandemic.

>“Meanwhile, housing costs are rising faster than incomes,” points out Bill Fulton, the director of the Kinder Institute for Urban Research, a think tank in the city, “And, as a result, a large majority of Houstonians have been shut out of homeownership and become renters, half of them rent-burdened, meaning they pay more than a third, and often more than half, of their income in rent.”

Hmm, now why does that sound familiar!?

>Houston has gotten this far by teaming with county agencies and persuading scores of local service providers, corporations and charitable nonprofits — organizations that often bicker and compete with one another — to row in unison. Together, they’ve gone all in on “housing first,” a practice, supported by decades of research, that moves the most vulnerable people straight from the streets into apartments, not into shelters, and without first requiring them to wean themselves off drugs or complete a 12-step program or find God or a job.

OP seems to read this part and conclude that "housing first" means just building more housing, except what "Housing First" really means is:

>an intervention for homeless people with severe disabling conditions that combines four elements: “(1) program philo- sophy and practice values emphasizing consumer choice; (2) commu- nity based mobile support services; and (3) permanent scatter-site housing... Because [Housing First] does not require psychiatric treat- ment or sobriety as a precondition for attaining housing, the model includes a fourth component, harm reduction, so that support services can help reduce the risks associated with psychiatric or addiction-re- lated behavior”

Yeah the long and short of it is we need to address the missing middle, and there's no incentive for private developers to do that. Doing things like changing zoning regs that require more affordable housing and allow for more housing types to be built might be somewhat helpful, but there's really no solution to the housing crisis that doesn't involve building more public housing.