Los Angeles, whose population is only 50% higher than Houston, has 25x as many people who are homeless (75k vs 3k).
If people couldn't afford food because there wasn't enough food grown, no one would think handing out food stamps would work. It's silly to think that doesn't work for housing.
These may be accurate and real, but I also wonder if this might partially be because Houston sucks in terms of lived experience for the homeless so they tend to end up elsewhere?
Texas has a recent and storied history of just busing people out of state or into other cities for people it deems are problematic or they don't want to deal with. So it would not surprise me if some of the stats are cooked or they've partially swept the problem under the rug.
I gave actual stats. They also match my impressions driving around both cities. If you have stats about the scale of busing people out of state please do share.
What you've suggested may account for some of the difference. But "Houston has liberal zoning and builds more houses" is a far simpler explanation for the staggering 25x difference in homeless population between the cities.