Does it even make sense for a city like Houston to have parking minimums at all?

Personally, I don't think it makes sense. By eschewing zoning votes numerous times, the city already made the commitment regarding favor of the market process. I think we might as well go all the way, and abolish any and all regulations still lingering.

More specifically, the stuff w/regards to urban development needs reform. From what I understand, despite the lack of zoning, it seems that lingering regulations do play a role in limiting the density and walkability that might otherwise come out of it. And it seems that the most crucial one appears to be the parking minimums: they skew out alot regarding the "missing middle" (limited to townhomes here as of recent, not much multiplexes) and "mix use" (autocentric strips vs street-level retail) that might otherwise be far more pervasive here.

Road and block widths are another problem, though that is mostly relagated for new "greenfields" (as opposed to city-limits development that tends to be infill/"grayfield")

It seems that setbacks do have more variances regarding the outcome. And for the lot sizes, that seems to be where the city made the most reform so far — I recall reading about the success of the late 90s policy changes that allowed the townhomes to take over to begin with (along with the extension out the Beltway 8 during 2013). It'd be interesting to see what the city can do with multiplexes considering that path alone.

The city did make changes for parking requirements, as they extended the exempt area from downtown into EaDo and Midtown in 2019. I believe absent/reduced parking minimums are also occuring in proximity to transit lines, with exemptions along primary streets, with reduced requirements on secondaries. Not sure if this is strictly for rail, or if it also accomodates bus lines, though.

But ideally? I'd like to see parking minimums abolished city-wide: yeah, even out to NASA/Clear Lake City.