I think this sort of development is a symptom of the largely inflexible nature of land use policies in the US. Since for the most part, the US is stuck with regressive policies like parking minimums and single family zoning. In our current state, it takes a private company to get past the bureaucracy. I think this shows that if there was a solid push for land use reforms, we wouldn't need a private company to make livable, walkable cities. The market does exist for this kind of living in the US, even in a state like Arizona.
Honestly I can see a future where privately developed and owned enclaves may become the norm since as you say, it gives a rather high level of control to a company in terms of who lives there, who works there, etc. I imagine that this could be a very lucrative business model, especially without guardrails, like the US likes to do.
As a side note, I peeked at the Tempe zoning maps where this development is sited, and of note is the fact that this is built right next to the light rail which helps with carless living. The development is one of the few areas that are zoned mixed-use in Tempe, most of which are also located near the light rail. It seems like there are a lot of plans in store for that light rail but it goes slowly as it always does in the US