You're treating this as a system which changes states instantly. It does not. You can progressively build housing and expand a city such that you can keep price

You're treating this as a system which changes states instantly. It does not. You can progressively build housing and expand a city such that you can keep prices stable, at least in theory, and 'affordable' (not a well defined word). In that sense 'overpopulation' is a deficient state which would not exist if not for heavy intervention against the natural response which would be to build at, more or less, the rate at which new residents are wanting to come. I'm not sure if there's a known limit to this, although I admit populations might oscillate a bit if SF with 100 million people is too unpleasant... That's not to say it's always bad to keep prices higher. Basic regulations do that (e.g. safety) and place a floor on the extent to which housing can truly be affordable without governments just forcing rent control and denying others the chance to live in a particular place entirely.