I'm sorry, but I completely disagree. A market based solution has no reassurance whatsoever that this would happen. As I said, markets only work to find the solution that makes more money for those with capital. That does not mean that it will be the best solution for those that actually live there. It's just as likely that a piece of property would be turned into a trash dump or strip club than it would be turned into a grocery market.
That's currently what we have; nothing at all resembling a free market where you can buy a piece of property and more or less do what you want with it. The rules and regulations in place are absolutely about enshrining the car-centric city.
With a more market-oriented solution, some people could have their "burbs" and others could have other kinds of housing and neighborhoods.