The wealthy paid taxes on their wealth back when it was income. And they pay capital gains tax if their wealth grows.
This is a game as old as the US income tax itself; the 16th Amendment wasn't passed to legalize income taxes (they were already legal), but to make sure Congress could tax income "from whatever source derived", since wealthy people were restructuring their income streams to try to avoid taxation.
They still do that today.
In any case, a wealth tax would be easy to game too. There is a lot of room for loopholes in the definition of wealth, what kind of wealth should be taxed, what the tax brackets should be, what kinds of deductions are allowed, etc.
I'm worried about the decline of the inheritance tax. It's happening all over the West. In France, "the incomes attained by the top 1% of French inheritors are already higher than those attained by the top 1% of workers".
We could be headed back to a Jane Austen -esque society where ambitious young people seek their fortunes in marriage, rather than in business.
There is a reason that investment firms exist: this process is a ratchet for making untaxed (or less-taxed) income.
If you pay them with income, you paid income tax.
If you pay them by liquidating assets (including assets you purchased with the loan money and then sold), you pay capital gains tax (unless you sell for a loss).