One often overlooked issue with a wealth tax is the damaging effect on financial privacy.
The income tax already has the IRS probing into nooks and crannies it has no business probing. It deputizes law-abiding businesses to snitch on each other through the obligation to report payments.
A wealth tax would ratchet the surveillance up even further. Not, not just income statements, but asset statements would be required. Enforcement would likely require reams of new compulsory snitching laws for sellers of property. It's not an outcome I think many respondents have though through much because privacy still flies well below the radar in the US.
Then there are unintended consequences. If you tax income, it re-appears as capital appreciation. If you tax assets, they will re-appear as invisible wealth. That's an outcome for which I doubt most in the country are prepared.