Why should a city subsidize housing? That seems like something the market should drive primarily. For that same reason, I'm skeptical about whether zoning and permiting are a good thing in general.
Zoning and permitting are a good thing. It means a city can have long term planning and allocate resources and budget things accordingly. Mishmosh cities have existed and do currently exist in emerging economies, they tend to be chaotic and crime ridden messes.
That said, I think zoning needs to be updated to reflect more modern economies. Mixed use, company housing (it's had a stained past, but still it can work, if governed properly), and the permitting should be less political and very much so more pragmatic. I rather detest the politization that has overtaken infrastructure building when it involves private investment.
With regard to subsidized housing, I think we need it to allow the poor to afford a place to live. Now, I don't think anyone has a "right" to live in a particular place, but you also should want to facilitate people of all sorts of income levels to live in a given municipality.
I'm not claiming diversity of vibrancy or any other pseudo reason people like to list, as they are based on feel good emotions. In addition, there are plenty of places that are very monocultural and are very vibrant (Tokyo) but at the same time we should try to include a diversity of strata and allow for people to move into the mainstream stratum, as most seek to achieve, in the fist place.
Well, if cities control the zoning, they then have to ensure for the welfare of the housing market. If you, for example, block developers from adding more housing (cough San Francisco), you are supporting raising housing costs and pushing lower income citizens out of your city.
If the market should drive the equation and the municipality meddle with either side of it, it's not a market in the way one normally infers.