Many, ... most? states have some kind of homesteading tax relief.
For example, in Florida property tax increases are capped to the lesser of 3% or CPI. 25k of value is also exempted from property taxes and 50k is exempted from non-school property taxes. But only for a single primary residential property.
Where CA13 is different is that it applies to everything: commercial property, industrial property, rental property, second homes, third homes, etc.
I think there is a pretty good case to be made that there is a massive public interest in keeping people from being pushed out of their homes by taxes. Capping tax increases is also necessary to make it possible to financially plan for them (e.g. I can invest enough so that my investments will pay the taxes w/ increases for the rest of my life, and just add that to the 'cost' of the home-- given historical market returns this requires investment of 25x your annual property taxes, so long as they can't grow faster than inflation). One could also make the case for a public interest in not letting some businesses get pushed out (primarily small, single location businesses).
But prop 13 goes far beyond that-- applying to all property and with extremely expansive portability-- and as a result creates a massive windfall for existing property owners at the expense of new property owners.
I'd like to see at least a rule that for rented properties that assessments should be allowed to increase as much as rents have. There is little to no prevent-displacement justification for not tracking rents.