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You're absolutely right that what most politically engaged people want is to preserve the status quo. So they will use increased social control over housing production the same way they're using existing social control over housing production: to minimize it. Existing NIMBY communities won't allow significant new housing. They're certainly not going to initiate and pay for it. The housing shortage is exactly the same thing as these people getting what they want, neighborhoods and communities that look and feel the same over time, excluding however many former/would-be residents they need to exclude for that to happen.

De-commodified housing gives a community more control over who gets to be a resident, but there's no reason it would lead to a change in how many. Expensive cities already have the levers for that.