Developers are not dumb, they can figure out what kind of parking is needed for their building without the power of law.
> It is the 4th largest city in the US and has almost no public transportation. Building an apartment that houses 1000 adults guarantees that 1000 cars that will need to be parked nearby.
This is a self-fulfilling prophecy; the more you prioritize car use with requirements for large garages, large surface lots, and large, wide, high speed roads, the more you make transit and walking slower and less effective, and the more you drive people into cars.
Houston has very high parking requirements that are actually even higher than what you are describing; even for "micro-apartments", an apartment size characterized by ~2-300 sq ft total space that could probably only fit one person comfortably, the Houston code requires more than one parking space per unit. https://www.houstontx.gov/planning/DevelopRegs/docs_pdfs/Req...
One market-based hint that the parking requirements are too high in most cities is that developers nearly always only build the minimum; if more was required you'd expect more people to go and above minimum requirements.