I think if the value increase cap was raised (gradually) to something like 4-5% per year, you would still have assessed values trailing market values, but not by nearly as much. People could still make worst case projections of taxes to see if they could afford things.
Washington state has a different system, where the total property tax of each taxing jurisdiction can only increase by 1% each year (subject to exceptions and what not), and then that amount is apportioned to each property based on the assessed value. This provides a limit on government spending as CA prop 13 does, but it doesn't limit changes in tax on any individual homeowner; if your property becomes more relatively valuable than others in your taxing districts, your bill goes up and theirs goes down. Which I'm sure causes assessments to be a lot more contenious.