But that's what they do! The ultrarich of the world can live handsomely off the interest of their fortunes and don't ever have to touch the principal, which just grows and grows.
That money still goes somewhere. You don't get interest by keeping money under your mattress. You get interest by loaning it out, or the value of something you own increasing. And even if you've "bought" something that appreciates in value, you've anyways lost the physical money which is now being spent by someone else.
Which is almost the same scenario as the one you suggested. So ultimately, it seems your complaint is not of the money being used/spread/churning throughout the economy, rather than being hoarded under the mattress. But rather, it seems you're complaint is with the fact that the rich have it and it's not being taxed for purposes you deem useful.
If I keep a million dollars in the bank, the bank can loan out a million dollars, and I earn interest.
If I spent half of that million dollars, then whoever got paid likely puts the money back in the bank and the bank can still loan out a million dollars.
This is in a nutshell why trickle-down economics don't work.
Families this rich are not just static forever, they usually have lots of ventures and businesses that are contributing to their wealth. They are well invested, but that's not the only thing.
They also do spend and consume a very high amount and there is the inevitable dilution through the generations as families grow and each person uses their fortune in a different way.
Which is almost the same scenario as the one you suggested. So ultimately, it seems your complaint is not of the money being used/spread/churning throughout the economy, rather than being hoarded under the mattress. But rather, it seems you're complaint is with the fact that the rich have it and it's not being taxed for purposes you deem useful.