The simplicity of this post notwithstanding, I think wealth taxes are the wrong tool for reducing inequality (the main reasoning behind its support): 1) it is difficult to implement, and 2) it disincentivizes economic activity.
The right taxation tool for tackling inequality is Land Value Taxation [0].
Some observations of our current situation:
1. The income gap between capital and labor that has been growing since the 1970s (as observed by, e.g. Piketty) is largely due to housing [1]
2. Economic growth and opportunity is increasingly concentrated in the the urban areas (and even within cities, a handful of them are responsible for most of the growth), however, zoning laws makes it very difficult to build new housing there and thus for rural labor to join the economic party. Thus, as we concentrate economic activity we explicitly exclude huge swaths of the population from participating in it.
3. With finite land, concentrated opportunities (i.e. no viable alternatives [2]), and overt house building restrictions, workers who do have the opportunity to work in urban areas are "willing" to pay the absurdly high rents that landowners ask. You can clearly see this in the Bay Area where, prior to COVID-19, the rents would just track the income level of tech employees. The current landowners are the main winners of the success of the urban areas.
4. On top of that (and specific to the USA), if a landowner decides to sell a property, the sale will be taxed as a capital gain which has a lower tax rate than the labor rate. We are literally incentivizing rent-seeking.
A Land Value Tax (LVT) taxes the value of the land (rather than that of the property). This has the following benefits:
1. It incentivizes more efficient usage of the land (a single family house and a high-rise pay the same tax if the have the same footprint and are next to each other).
2. Land is finite, so it can't "disincentivize" land production.
3. When land appreciates, it is rarely if ever because the owner invested in it, rather because the economy around it makes it more valuable. This tax captures that value and returns it to the community (rather than privatizing it and giving it to the landowner).
4. It is a progressive tax.
Instead of arguing whether and how to implement a wealth tax, we should pursue a national LVT.
[0] https://en.wikipedia.org/wiki/Land_value_tax
[1] https://www.brookings.edu/bpea-articles/deciphering-the-fall...
[2] Technically, you can choose from a set of successful cities, but they all follow similar patterns.