Fair is fair
This is a no-brainer! The property value for city purchase or eminent domain is the appraised value you have agreed to when you paid your tax bill. We should pay no more than 10% over that value.
In fact it should be routine that, upon change in ownership (or responsible tax party), a seven year look-back is done. Any difference between the selling price of the property and the appraisal for tax purposes of the property should result in the difference being amortized over seven years (or the time since a major reported or permitted improvement), the taxes recalculated and the difference due immediately.
This would minimize under-valuations and raise the amount collected annually. It would minimize the cost to the taxpayer for acquisition. Wise owners would make sure that their valuation for taxes comported with their valuation for insurance and with what they would expect for purchase. Fair is fair.