For a certain set of cities (the set of cities called World Cities) diversity can work, if managed properly. In all other places diversity is a net loss.
There are many requirements of a people to properly manage diversity, and be a Global City
Houston's lack of zoning is a result of a unique culture of openness, property rights and rule of law. This is because zoning is a bottom up phenomenon. Only a culture that values freedom can become a successful World City.
Most Citizens of other cities value the static nature of zoning, preventing others from doing stuff on their land. Not the case in Houston; for in Houston land use is determined by developers seeking to make the most money by serving the needs of paying customers. Why would someone put a crack shack in a nice neighborhood, even out of spite, it would be cutting your own nose to spite ones face.
So in actuality you are in greater risk of bad development under zoning, even strict zoning. This is because Zoning is opposed to the Rule Of Law. Therefore if you are not politically connected the planners do not care about what you want. So then they might throw a low income housing project on your street to meet the plan objectives.
The rule of law is important so that people are willing to risk their capital. In most cities in the world you are under risk of rezoning. If one is not politically connected you may see more density you expected for them to allow. In adition one will run into the permiting nightmare of the NIMBY army, and be prevented from building anything.