> Why not make it a multistory building with apartments on top of the supermarket and skip the parking space or put it underground?
That's exactly what they are doing at a few places in my city (also with a massive housing problem).
We recently found a new apartment here, the process was as follows:
(1) We found the apartment online. It was online for exactly 6 hours, listed by an estate agent.
(2) Inside the listing (hidden deep in the description) was a short sentence saying that any contact made through the listing website contact form would be ignored and that a secret mail address had to be used. You had to email an application letter (preferably with photos), copies of your latest 3 salary statements, copies of your identity card, proof of your credit-worthiness ("Schufa-Auskunft" in Germany), proof that you had liability insurance, and contact information of previous landlords. This had to be mailed until a deadline the next morning. If any of this was missing, the application would be ignored.
(3) A week later, we received an email telling us that we were eligible for an appointment to visit the apartment. But we had to confirm this until the same evening by sending an SMS to a secret number.
(4) A few days later, we indeed got a date and time for visiting the apartment (via SMS). It was a 15-minute slot, but there were at least 10 other families there, and they did visits the entire day. When the agent asked us, we indicated strong interest, told him we could rent the place beginning tomorrow and left.
(5) A week later, we got the apartment (of course we now have to pay 2 rents for 3 months). When we asked him why the process was so complicated, he told us that they were only 4 people in the agency, and they didn't have the capacity to read (not answer!) > 1000 mails of people interested in the apartment. So they gradually came up with various hoops and obstacles to get this number down to something manageable (they got it down to around 50 families who indicated final interest).