Wealth Tax
I am against any wealth tax. The revenue services for many governments are very focused on not blocking economic growth, and then periodically taking a reasonable amount of wealth.
In the end, only wealth can be taxed (things that aren't physical can't be seized and auctioned). However, I don't want to be forced to let someone into my house to calculate how much stuff I have.
In general, I think it’s more reasonable to monitor wealth moving (and more so if wealth moves between people) rather than to force people to cooperate with monitoring wealth staying in the same place. I don’t want someone checking up on whether I own the same stock certificates or gold bars each year; that seems like an insult to my dignity.
Enforcement Complications
Distribution
The top 10% as a whole pays 71.22%, while the bottom 50% of taxpayers account for only 2.89% of all income taxes.
I don't think that focusing on people who already pay a disproportionate amount of tax will be very helpful. Rapidly changing what is taxed (wealth vs income) would probably be harmful, as people will probably have trouble adapting to significantly different policies. For example, we'd probably hear about people who happen to have inherited expensive houses being unable to pay thousands of dollars for tax bills, after thinking that they wouldn't be affected by policy changes.
Avoidance
If there was a wealth tax and I was rich enough to spend a lot of time managing my money, I would just create a "charitable organization" that I and my family completely control, then have it pay people to do things I would want them to do anyway, and maybe even try to let the charity pay a high wage to its managers (such that I could be a manager and get the charity to pay for my yearly living expenses, directly or indirectly). I also might be able to get away with using a trust or charitable remainder trust to avoid being affected by a wealth tax.
I don't know the degree to which tax exempt organizations affect my life, but I do know that trusts have a relevant affect on my life, since they are often used to own land, specifically by landlords of housing and by people who own land that is worth a lot of money. How they are dealt with would probably have to significantly change in order to accommodate a wealth tax.
Inheritance Tax
I'm not sure I'm against inheritance tax, but it might be an unnecessary complication. Treating inheritance like a gift from one person to another at the moment of their death might make things easier for everyone. The policies regarding gifts are relatively clear: https://www.irs.gov/businesses/small-businesses-self-employed/gift-tax https://www.irs.gov/faqs/capital-gains-losses-and-sale-of-home/property-basis-sale-of-home-etc/property-basis-sale-of-home-etc
However, having separate inheritance law might also make things less painful for some people. If my assets suddenly gained or lost a large amount of value just before I died, I wouldn't want that to justify taking more wealth from my heirs. Having a special way to value assets gained due to someone dying might be more reasonable than treating each receipt as a gift.