This argument comes up almost every time and it has never made any sense to me. Yes, you would rather live than never have been born. That's because you're alive right now, you can have and express that feeling. Someone who doesn't exist will not care even in the slightest, because they can't.
There are dozens of appicants for each flat anyway, with or without the cap.
Not everyone can just buy a place, if rents keep increasing only rich people will be able to afford living in the city, you need a lot of non-rich people to actually run the city though: cashiers, nurses, teachers, firefighters etc. It's not that easy.