"Old" or "New" -Urbanism has never been about absolute property rights. City dwellers have, for generations, traded the conveniences of density over pure private property rights.
How would you feel about your next-door neighbor turning their home into a slaughterhouse or paper mill or adult bookstore?
Zoning is just one of many ways that people, through democratically elected governments, restrict private property rights in cities.
While Houston doesn't have formal zoning, a quick Google search (I've never been there) shows they do have extensive land-use regulation, including minimum lot size for single family homes (5000 sq feet) and requirements for parking for businesses.
So, if I wanted to place two single-family homes on my 9000 sq feet of land, or open a retail shop without providing parking, my private property rights would be infringed.
How would you feel about your next-door neighbor turning their home into a slaughterhouse or paper mill or adult bookstore?