A wealth tax is usually targeted at people with substantial assets. In the UK there is discussion of charging people with total assets of more than £10 m an annual levy of say 2% of the assets. This is a kind of income tax surcharge. If someone is managing to earn the current 4% return you could get on a bond it is effectively a 50% income tax on top of the 45% tax the rich are already paying. It means lower risk investing ceases to produce any return for a well off saver. How long before that saver goes somewhere else or at least stops financing the spendthrift UK government.
Wealth taxes elsewhere have led to the exit of rich people, as in France.They can lose the state more total tax revenue from departing millionaires than they recoup from those who stay to pay.When Labour last squeezed the rich in the 1970 s with a 98% tax on savings income there was a big exit called the brain drain. The state ran out of other peoples money to spend and had to beg a loan from the IMF. They imposed some spending cuts.
Charging on total wealth is complex and expensive to enforce and complex and expensive for the taxpayer. Much wealth owned by the very rich is in the form of property assets which generate no income and impose substantial costs on the owner. Many have a large home which is expensive to maintain, heat and run. Annual revaluation could be expensive and would be a matter of judgement as these properties are usually one offs with no ready market. People who own art or other valuables get no income from them and have maintenance and insurance costs. Some of the wealth is the consequence of someone now on a modest income or pension living in London house which they bought years again when they were more affordable. A wealth tax could force them to sell their family home as they may well not have the income to pay the state 2% of the value of their property. Enforcement will be difficult with smaller items of wealth like stamp and coin collections, gold, furniture and smaller works of art.These would all become more popular with the rich if more measurable and visible things were taxed, especially if they are left out of the wealth tax demands.