Would there be many? Certainly, there were some cases pre-prop 13, but prop 13 wasn't narrowly focussed on protecting homeowners. Those were exploited as pretext, they weren't the motivation.
And you could make it protect homeowners while fixing the local government incentives by providing a refundable state income tax credit for 100% of the property tax due to assessed value increases beyond the existing Prop 13 limits. You could do this without or without, modifying the 1% fixed rate.
If you don't want that big of a subsidy, you could just allow homeowners to defer without penalty the excess amount until transfer of the property. Still stops people from being priced out of their homes.
If we'd begun a phase out in 2000, during the height of the tech boom, then by now Prop 13 would be gone and the housing situation would be much different.
Prop13 is a monster that will continue to exacerbate inequality. Families that owned homes in affluent areas pre-1970 will continue to pay artificially suppressed property tax rates in perpetuity, so long as they only transfer the house within their immediate family. In that way, Prop13 is a perverse incentive to suppress real estate transactions, which exacerbates the real estate issues we already have.