Agreed, the biggest boom towns have been in the South where restrictions are low and profits high, leaving some really ugly suburbs.
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.
1. https://www.governing.com/housing/how-houston-cut-its-homele...
2. https://www.lahsa.org/news?article=1051-lahsa-releases-final...
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.
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.