It's a terrible system because a billionaire could come in and scoop up thousands of people's property for pennies (assuming they set their property price low because they can't afford tax when they set it higher).
It can work.
But, to your point: why shouldn’t people pay tax on the value of their property? If they can’t afford the tax, then obviously they can’t afford the house right? Prop 13 is already effectively a Ponzi scheme— actual tax cost is paid by future investors rather than the current investor. So if I buy a house today, my tax rate is x. Tomorrow, my tax rate is still x even if the actual cost of government and my home value has increased. So tomorrow’s buyer pays their tax plus the difference between my x and the actual tax required. Tomorrow’s buyer perpetually subsidizes yesterday’s buyer.
That isn’t fair at all.