Why should vacation homes be taxed? It’s is an asset. Imagine.. You buy a diamond ring..would you be asked to pay a use tax every time you wear it?
Yes. In addition to following the flurry of news articles every time some politician dares to bring up Prop 13, I grew up in the Bay Area, and in fact I studied Prop 13 along with its consequences and potential changes while at university. If you'd like to be pedantic, your words were "And then they try to change prop 13".
Nobody (at least nobody with any sort of visibility) has proposed repealing Prop 13 wholesale.
Prop 13 also pushes undue costs onto new property development. Lower development costs equals fewer luxury condos. Were California to both build more and repeal Prop 13 fully it's unlikely that retired tech bros would be priced out of their houses.
Even so one of the primary roles of a county assessor is to determine where tax breaks are suitable. Allowing the (typically elected) assessor more discretion via a Prop 13 repeal almost certainly guarantees you won't be putting grannies (or retired tech bros) out on the street.
I'm not going to bother digging into most of the rest of your claims but this is particularly disingenuous. Most of the recent attempts at changing Prop 13 have focused on a split roll that would keep the tax limits on primary residences. Putting grannie out on the street is exactly what the anti-tax zealots (Jarvis and co) used to sell the state on Prop 13 and 8 in the first place. What's being proposed now would raise taxes on things like vacation homes and commercial property.