All of this sounds well and good until you see the natural conclusion of those policies to keep old people from having to pay for their dragon hoarde. It turns your city into the Bay area where no one can afford to live there except the landed gentry you've created.
You need to fix the problem, but fixing it by Prop 13 has numerous issues. If it had been deferred as a lien against future sale/inheritance, or didn't apply to commercial properties, or ...
Fixing the "problem" of people not moving out when the area prices go up is exactly the problem itself.
The issue is availability of property flat out. As long as there's no incentive to make affordable property available, every actor wants their property values to rise and cares little for the negative effects it has on everything else.
Those property taxes exist for good reason because you have to be able to pay for the services / infrastructure from it. Without those matching the area, problematic spirals occur.
