Perhaps notable: Switzerland has a wealth tax (of up to 0.3%), and there is zero evidence that this has any deterrent effect on wealthy people settling in Switzerland or startups being created in Switzerland. Other features of the tax system more than offset the 0.3% wealth tax. Personally, I am a bit disappointed by the lack of depth of the discourse: Wealth taxes and their effect have been studied quite a bit in ec…
For one, it pushes people towards riskier investments. At a 1% annual return, a 0.3% wealth tax is equivalent to a 30% income tax. At a 5% annual return, it's equivalent to a 6% income tax. This has various consequences, but a big one of note is that it makes it much less desirable to own government debt, which has a low rate of return, which means the government could end up having to pay significantly higher interest on the debt. It could also incentivize excessive risk taking.
Another concern is that it requires investments to be liquidated in order to pay the tax. Generally we defer taxes on investment income until the investment is sold in order to avoid this, because it can be quite problematic, e.g. you own 51% of your company but over time you're forced to become a minority shareholder just in order to pay the tax, or you owned 100% of it and are required to take on external investment over time just to stay in business. This also costs the government money because the government pays lower interest on borrowing than average investment returns, so paying 0.7% to borrow money in the interim while the investor is earning 5% returns on the money you'd have collected as tax means that when the tax is ultimately paid, the government ends up with more additional revenue than they paid in interest in the meantime.
It also increases foreign ownership of domestic resources, because domestic owners are forced to liquidate in order to pay the tax and domestic buyers are in the same boat so the liquidated securities go primarily to foreign buyers.
Another problem is that a lot of forms of wealth are hard to value. If you had a wealth tax and someone owned a piece of art, or some intellectual property, or shares in a privately held company, what are they worth? It's inherently subjective and estimates can very wildly. But then you're creating an opportunity for accountants to do their thing and avoid the tax. Waiting until the property is sold and then taxing the gain solves this neatly because then you have the sale price to go on.