This is another variation on the old "rich people hoard cash" trope.
Rich people invest the money that they don't spend. They tend to invest well, meaning highly productive investments, because (naturally) wealthy people get wealthy by being good at investing.
Productive investments are good for the economy. The notion that wealthy people invest in unproductive things doesn't make any sense.
[Citation needed]. There's lots of wealthy people who got funded, got lucky (some investments are good only looking back - would you like to pay me to sign a few bytes 7 years ago?), got family fund, play the right sport in the right country, etc. People can get continuously more wealthy just by owning things - at that point you can outsource the investing to someone good at it. We've got very well known examples of people who inherited fortunes, failed at investing it multiple times and are still wealthy.
See "The Millionaire Next Door" by Stanley
It stands to reason that if wealthy people as a group are bad at investing, they'd sooner or later stop being wealthy. Then, by survivorship bias, the wealthy ones remaining were good at investing.
Right now they will use any savings to buy back stock - that's the rational thing to do and makes the investors happy. But if we tax investment income progressively then buying back stock is great for the US Treasury - someone has to sell that stock to the company buying it back and it's taxed more!
It becomes more reasonable to reinvest that money from a corporate perspective. This is what the investors will want done.
It seems you imagine that isn't actual investment. Of course it is, just like anyone else buying stock is investing the money.
One aspect of wealth is that it's a capture of some local increase in human-useful efficiency. The most common use of large amounts of wealth is to buy more capital. All systems have a limit to their efficiency, and even when efficiency improvements are possible, it's often not obvious or easy to achieve them. What is easier, though, is to decrease efficiency in a neighborhood you do not own, and then use capital to provide a more efficient solution to that neighborhood's problem in a neighborhood you do own. Clearly this is bad for the greater economy, yet is a good investment for the foreseeable future for those who can afford it.
Are they? Or are you defining "productive" circularly here?
If I'm wealthy and I invest in derivatives or complicated tranches, is that "productive" because it's enabling further circulation of money, or is it "productive" because I can gain more capital on it?
Given that there's an infinite supply of ever more derived tranches, I suspect that my definition of "productive" different from yours here.
Analogously to a flying airplane - it is producing more lift than its weight. This must be true even if you haven't the slightest idea how all the whorls of air and eddies around it are created or how they influence the airplane.
What derivatives do is they spread risk in exchange for a lower rate of return, as well as provide liquidity. This is a productive thing that financial markets provide.
It can under a fiat money system (which we've had since 1914). If you or I borrow money, we have to pay it back. That's not so for the government with fiat money. It can just print more money anytime, or do the equivalent (issue more bonds), and it can do this forever.
This is why the dollar today is worth just a few cents of what it was worth in 1914. (The 1914 dollar was worth the same as the 1800 dollar.)
Check out "Monetary History of the United States" by Friedman.