No they don't. From what I've read (Piketty etc) they do not re-circulate it into the general economy. They use investment vehicles which are increasingly divorced from "real world" economics and more like moving chips around on a poker table. It's wealth in the service of wealth creation. All of that happens in an almost separate level of the economy. No poor or middle class person is even involved.

I'd "hazard a guess" that wealthy investors might be more effective at creating more wealth, but not at raising the standard of living of the countries they are in. In fact, the standard of living in the United States is declining.

Approximately 100% of the money that poor and middle class people spend goes to corporations. If you give them money, they spend it on goods and services. That's pretty efficient.

The alternative, if you tax the rich, is that the same money flows to the government and the government spends it on programs.

Is that the only alternative? At this point, probably. I don't trust the government either, it's a bloated plutocracy. But you could still make a completely economic/utility theory argument that the benefit to 100M+ people outweighs the overall good for the 1K+ people at the top of the current hierarchy.