Can you help me understand how #1 becomes #2?
With prop 13, the downside is wiped out. Increasing values are only good; they could increase 10x overnight and this would only make landowners filthy rich, there's no negative effect for them. Ergo, they have every incentive to keep housing supply constrained, to keep voting for politicians and policies that limit housing density.
Another way to think about property taxes is that they're annual nudges to encourage best use of the property.
Without that pressure, as TulliusCicero notes, why would I ever sell before retirement? And furthermore, why would I even try to make money off the property (say, by renting)?
That's probably not in the city's (as in, all the people living there) best interest to have a substantial portion of homeowners so disengaged from the actual market.
PS: Which isn't to say there aren't gentrification and affordable housing debates to be had. Simply that Prop 13 doesn't really help with that -- it just removed risk from those who are already homeowners.