Currently investment is only taxed on a "realized basis". No tax bill is due until the investor realizes a cash profit, either by receiving a dividend or harvesting capital gains on sale of the asset. In contrast a wealth tax is assessed every year, regardless of whether the investor has actually earned any actual income.
Under current tax law, an investor is not penalized for continuing to hold a high-value asset. In contrast under a wealth tax regime, an investor would be forced to sell some portion of his portfolio every year just to pay his tax bill. That heavily favors large, liquid, public companies over startups. Selling a million dollars of Amazon shares is as easy as pressing a button. Selling a million dollars of a Series-A startup, especially at a fair price, is really hard.
This would especially impact early-stage employees, who usually hold a very high fraction of their net worth in their stock options. At least VC investors usually have other holdings that they could liquidate to pay their annual wealth tax.
Imagine you own 20% of a company with a $50 million valuation. On paper, you're a deca-millionaire. But in reality you could easily have an overdrawn checking account. How do you get your hands on $100k in cash to pay your tax bill? There's no real market to sell your shares, and very likely you can't even do so without board approval. You could borrow the money, but if the company fails, you're now left with huge debt and worthless equity.
In all likelihood a wealth tax would pretty much destroy the Silicon Valley startup ecosystem. Or at least remake it into something totally unrecognizable.
A wealth tax does not reduce income, it reduces wealth! Income taxes and capital gains taxes reduce income.
But taxes provide services that give people a greater safety net. Healthcare is the canonical example but there are many other ways that taxes can help ensure that one mistake does not ruin the rest of your life.
Personally, I would love to live in a country where businesses took fewer risks and individuals could take more.
It doesn't seem like low risk investments like sticking money in the bank to be lent as mortgages or investing in government bonds are as good for humanity over the long term.
Wealthy people don't just leave their money under a mattress, they invest it in something. Even if they just left it in a bank, the bank is still going to lend that money out and invest it. Taxing wealth just encourages riskier investments, as higher risk is needed to achieve comparable post-tax return.