> I think something like California's Prop 13 that puts a cap on property tax increases is a better idea

Prop 13 is one of the worst ideas in taxation ever. It would be better just to let the aged and disabled freely defer property taxes beyond a certain, income-based level (and maybe also to let other people do the same with certain limits on total deferred amount relative to assessed value for time-unlimited deferrals, and total time for value-unlimited deferrals.)