That's not how any of this works. Rich people generally have much less of their assets as cash or cash-equivalent than poor people. They also in general have much more debt than poor people, both in absolute values and as proportion of their net worth. (Simply because they are able to take more debt, and with the neverending low interest rates, taking more debt and investing it is basically free money.)
If it's in a bank account, it's being lent out and is working, no?
I'm not understanding your logic - it seems backward to me.
Also we have never actually done "trickle down", it's a bogyman people like to trot out, not something actually done.
I also agree that they have debt for that as well. No reason not to use debt to gain real assets when the fiat debt loses value regularly.