The purpose of the wealth tax is to tax wealth.
The higher the inequality, the more it hurts if wealth is not taxable because it means less and less assets and money circulation are accessible to be tax and thus to pay for the gouvernment expenses. There is a limit on how much you reasonably tax work before that is crippling the economy. And a wealth tax would not burden the middle class or their retirement plans at all. Similarly to inheritance tax there would be thresholds under which no tax occurs.
Sure, wealth tax has problems. One of them is the potential to drive wealthy residents out. Another one is that, indeed, it is inefficient because it would require to know how wealthy people actually are and estimate countless items that are not actually on the market. That is a huge bureaucratic undertaking and leaves lots of room for shady practices or unfairness (like, again, inheritance tax).
It is still worth it just to combat inequality. How else are we ever supposed to get rid of inequality or at least lower it ? It won't get better by itself, only worse because capitalism leads to wealth concentration.
You're confounding hypothetical wealth and money supply. The two things aren't linked 1:1, ie someone share increasing in value doesn't mean that an equivalent amount of money disappeared from society. Lets look at it in a different way, so you own an house that you brought a long time ago, suddenly its discovered that under your house there's a massive amount of gold, equivalent to 1 trillions dollars, making you technically a trillionaire. How does that reduce the amount of money circulating and accessible to be tax? How does this reduce the ability of government to function? While this increase inequality in society, how is that a problem? Who are the people negatively affected by this? Why is it so important that the government immediately start taxing you on that value even if you don't use the gold?
Like you said, inequality is a problem when its taking money out of the economy, but almost all extremely rich people aren't rich because they cash their share right away and have a giant Scrooge McDuck money pool that they hoard. They own share who they buy at low value and keep while their value increase, which doesn't cost anyone anything.
Hang on a second, stop there, because there's a lot wrong with this.
Firstly, there're dozens of mechanisms by which a wealth tax can avoid being affected by wild fluctuation.
Secondly, if the value of their holding reliably increases, then that's an asset with a monetary value-- accounting it as a part of their wealth makes sense. The extra value didn't come from nowhere, and it certainly wasn't created when the government taxed the holder.
If they don't sell it? Then the government is receiving an existing 100m the holder already had. And if they do sell it? Then the 100m isn't "created" by the revaluation; the share price is transferred from the buyer to the seller, and then (in part) to the government. None of this is the same as printing money.
But the extra value did come from nowhere. Like Jeff Bozo has a bunch of amazon shares, most of these hes had since the beginning and never sold, these have greatly increase in value. If that extra value didn't come from nowhere, where did it come from? Who lost all of that money for him to become richer?
Or, lets look at it the opposite way, the government would use that tax money to do something. But if they didn't tax it, Bezo wouldn't have done anything with it, so this would obviously drive inflation, like if the money had been printed. You might say that Bozo could sell the shares at anytime and then start using the money created, which is absolutely true, but then he would be tax at that point on the gain he made then and there.
Now I'm not against increasing capital tax (which is shamefully low) or some form of wealth tax (I think inheritance tax should be much higher with far less loophole, but only because it doesn't require constantly recalculating someone value every year and require goods to be actively transferred). I also think there are plenty of other way to raise revenue that mainly benefit rich that should be explored (church should pay tax, charity donation shouldn't be tax deductible, private individual shouldn't be able to make company and use these to deduct their personal tax). But the "soak the rich just to soak the rich" mentality doesn't serve much purpose and can be very destructive to society.
