For example, let's say you own a car with an appraised value of $25,000—meaning that you could buy one similar to your for that price (more or less). So you declare the taxable value to be $25,000 and pay the corresponding tax, and then right before you leave for an extended road trip someone decides that they would rather have your vehicle than one from a dealer and makes you an offer for $25,000 which you cannot legally refuse. Now you're without a car and scrambling to buy a replacement and get it registered, insured, packed, and ready to leave on short notice. Your plans are disrupted and the new vehicle, while "equivalent" to the one you had before in terms of factory specs and general condition, just isn't the same as the one you had carefully maintained and customized to your liking.
In practice people would need to over-declare the value of any property they didn't want to sell, which effectively makes this a tax on how attached people are to specific items and not a tax on their "fair" market value. The situation becomes even worse if the owner has enemies willing to over-pay for the item purely out of spite.
One of the fundamental rights of ownership is the right to choose not to sell, no matter how much someone offers.
If we think that "everyone" will have to "overdeclare" in such fashion, then obviously the government is collecting more revenue than it intended and will lower the tax rates to compensate, so in the end, you'll pay the same dollar amount in tax on your $26,000 car as you would have on your $25,000 car.
So, such a system would work fine. Particularly for property taxes, which are currently the subject of much scamming (apartment buildings in NYC being valued at a few percent of their actual market value, for example).
If everyone over-declares by the same amount, sure. But not everyone will. It depends on how much attachment one has to a specific item, how much risk there is that someone will attempt to take it, and how painful or inconvenient it would be to lose it. And you're ignoring the point about being vulnerable to motivated individuals willing to pay above-market rates purely to cause trouble.
You get to declare a reasonable value, and if someone wants to buy, but you're not willing to sell at that time, the insurance company negotiates a substitute payment, and works that cost into your retention rider rate going forward.
Piss someone off? Maybe they'll just come in and buy your house. Cherished one of a kind item? Jeff Bezos likes it, so it's his now. Property developer wants to build something on your land? Get ready to move, no questions asked.
Any item must be purchased at a +30% premium over the recorded value with that extra 30% going to the state if a sale occurs. So if you did want to hold onto something, you would declare a higher value and get paid extra.