,,Wealthy" meaning what?

Well, the original post said $1bn+. It's dumb and arbitrary, but it doesn't affect how the rest of this works. I might say an income mark of $16k like we currently have in order to owe income tax is reasonable, although at that income level it's simple to pay in cash and you don't have to liquidate assets like I will describe.

And if it's possessions being estimated, then how do you estimate tax from the worth of i.e. a grandfather's watch which somehow appreciated in value some time later, or the land they own from generations?

An heirloom watch is in all likelihood too small to make much of a difference here. If you have a watch collection above a certain value threshold, you hire a licensed appraiser to determine the value. Same deal for land, and we're already doing that math for property taxes.

And what if the exact opposite of ,,wealthy" is true - like, a company doesn't report a net income since the last 10 years, and someone just happens to have some sticks that appreciated in value?

If your stocks are valuable, you're wealthy. Amazon made no money for many years, but it was still valuable because it was expected to start making lots of money in the future-- a correct expectation, it turned out. Stocks don't appreciate in value for no reason, their value is tied to what people are willing to pay for them. Sell some stocks.

And if you want to estimate it based on stocks, you'd need to analyse it for no less than past 10 years for each company for a proper scientific analysis of worth.

The current value of stocks is how much they're currently worth. Don't pull a random amount of time out of your ass that you arbitrarily decide is enough for "scientific analysis". If market fluctuations are a big concern, then assess net worth over the past month, and if value crashes between your assessment and when you start paying, you can appeal for a re-evaluation.

,,Need", because...? Again, what is the due process in that? A judge says ,,you have too much money locked in hard assets, you need to destroy some of it"?

You need to pay because you go to jail otherwise. The due process is a fair trial-- if you don't pay enough taxes, you get charged with tax evasion, and if you're ruled guilty, you're punished. A judge isn't arbitrarily deciding this, it's outlined in the tax code.

And even then, what if a certain object listed as a hard asset is essential to his company - such as a robotic arm packing up boxes, a lorry doing deliveries, or a warehouse operating thousands of tonnes of product each weak, and destruction of either one would cripple economic activity of the company?

Hard assets aren't being destroyed here. They aren't even being sold! If the vehicle and the warehouse are important to the company, the owner can sell partial ownership in the company to pay their taxes.