Then prop 13 will meet its ostensible purpose -- so the elderly don't get forced out of their homes by taxes, while those that own investment properties pay taxes on the market value of their property.
(note that I say this as someone that owns a couple rental properties in the California and benefit from Prop 13)
One of my favorite alternatives is to bring back regular tax reassessments, but owners can choose to cede excess property value to the city/state. This forces a choice between having your cake and eating it too.
I lived in a rent controlled apartment in San Francisco, and about 30% of my neighbors were over the age of 60 including an 80 year old neighbor who'd been there for 40 years and had great stories to tell.
Then I lived in a 20 year old building with no rent control, and almost all of my neighbors were age 30 or below working in the tech field (few lived there for more than a couple years) -- with no elderly people that I was aware of. (we had a few months of of false fire alarm activations, so it was pretty easy to see all of the residents)
If we don't need the extra revenue from rising property values, we should cut property tax rates accordingly. City residents getting the same public services for a smaller percentage of their wealth would be an immensely positive impact of tech's prosperity.
If we do need it (and I suspect we do, because higher prices mean government facilities and staff are more expensive), we should collect it fairly across the board. Maybe "fair" means flat, maybe it means progressive, maybe it even means "tenure in city" or "tenure in neighborhood," but "tenure in current address" is crazy. At least use a mechanism with some thought put into its incentives and possible unintended consequences.