You shouldn't scrap it completely; you should limit it to primary residences (spend more than half the year there). That would get rid of some of the worse issues.
It shocks me every time I hear fellow left-of-center people talk about scrapping Prop 13, but then also rail against gentrification or some other issues. Absent Prop 13, people would literally be forced from their homes from high taxes.
Prop 13 was a response to the inflation of the 1970s that drove asset and investment prices higher.