Houston is the only major U.S. city without zoning. Does it matter? Some year ago, Bernard Siegan argued that it does not. He compared Dallas (with conventional zoning) to Houston, attempting a kind of "twins" study and found few appreciable differences.
Where there is no conventional zoning, there is still an understandable demand for property rules. Developers find ways to supply them. Where there is zoning, it is often shaped by development pressures.
I have not seen the Siegan comparison revisited, but Wendell Cox has been the keeper of urbanized area (UZA) population data from 1950-2000, so I looked there. To be sure, UZAs are bigger than cities, but they are functional (not political) boundaries that are adjusted every ten years (2010 data not yet available). And in each case, there are UZA jurisdictions beyond the core city; in 2000, the city of Houston was 51% of the UZA, for Dallas it was 29%.
In the attached, I looked at just the UZAs with more than 3-million pop in 2000. The data include square miles, so population densities can be studied. I have blogged many times that large-area densities are averages that include large variances so am always concerned when inferences are made about small-area attributes such as ease of mingling and networking. But that is not the point of this post.
In the spreadsheet, look at the five Sunbelt UZAs with a 2000 population above 3-million, the relevant comparison group for Houston and Dallas. It appears that (1) Dallas and Houston have more in common with each other than with the other Sunbelt UZAs; (2) Dallas was more dense in 1950, but has ever since been less dense (more "sprawling"?) than Houston; (3) their density differences have gotten smaller; (4) in 2000 they had about the SAME density. 2946 pop/sq-mi vs 2951 pop/sq-mi are well within any margin of measurement error.