I don't think that is going to solve anything.
IMO Germany needs the Danish mortgage system. It'll rip the banking sector a new one.
The Danish mortgage-credit system dates back more than 200 years. Many of the original principles still apply
jyskerealkredit.com
Public housing system in Denmark and Germany probably function similarly. but if the mortgage+interest is too high the rent will be high too.
That's where the beauty of Realkredit comes into play (Obl. = Bond). As you can se if you borrow 1 mio. dkk for 1 year the interest is 0,23.
You pay off your debt over 10, 15, 20, 30 years.
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The bond/debt are locked to a certain timeline and can't be changed. For public housing this kind of financing is better than bank loan/credit. Low interest and other costs, and they will in return mean low rent as newly built public housing can have cheapest possible financing e.g. 3xA rating.
It would require certain Social Democratic initiatives be implemented like in Denmark, public housing non-profit organization should be established. Union to oversee them.