There are some theoretical advantages to a wealth tax but in practice it would be extremely difficult to implement. The issue is that much wealth isn't cash in a bank account or holdings of publicly traded securities but rather equity in illiquid private investments. And some of that is offshore, so would you only tax wealth held in the USA by American citizens or would it apply more broadly?
Like one person I know is a German citizen living and working in the USA with a permanent resident visa, and she owns some forestry land in Canada. Should that land be subject to a wealth tax and if so how would you value it? Does the IRS then need to hire an army of bureaucrats to calculate valuations on those assets?