Forcing people to pay property tax on an inflated valuation of their house or face eviction sounds like a terrible system, actually. If you offered to buy my house for a number that I agreed was a perfectly fair market value that I didn't expect to be able to beat on the open market, I would say no immediately. You'd have to offer something like 50% over what I'd expect to get for me to seriously consider the offer.

It is very common to have goods where the price a buyer is willing to pay is smaller than the price a seller is willing to accept, and in a free market that simply results in no transaction happening. Forcing the transaction to happen is always going to make at least one side of the deal unhappy.