A big problem with wealth tax is that not all wealthy are what you think of as rich. Old grandma maybe lives in a nice house in a good area that her now dead husband bought for 2 pennies 60 years ago. Now that house is worth millions. That grandma is a multi millionaire, but she may have a very minimal pension. Wealth tax that house and she may have a larger wealth tax than her entire pension income and be forced to move out of her own home.
Another example would be many farmers. Most small farmers don't earn a lot. Some even go minus some years. But the land and machinery they own are worth extreme amounts of money if sold. Wealth tax them and they will go bankrupt.
So a wealth tax is a very uneven tax. It benefits those who don't save and those who own business which are not capital intensive. Why should a farmer pay a lot more tax than a work from home freelancer even though both may have the same income?
There are so many weird things that can happen. Imagine you own a small property of land. Then they discover oil on your property. Suddenly you are wealth taxed for an extreme amount of money even though you don't even want to let anyone drill for oil on that land. Maybe you will even be forced out of that land because suddenly you can't pay the wealth tax on it.