What you're really complaining about is the bank lending out money. There is no way to know if deposit X+1 is money that was already loaned out. Your accounting of the work done is plain wrong - each of the people in the chain (person Y for example) did some real work and got paid for it (otherwise why did X pay Y at all?). If whomever paid you the $100 got it from a bank, that doesn't invalidate the work you did.

What you're describing is related to the "velocity of money" and "propensity to save" which are odd concepts but also one of the most direct ways behavior effects the economy.

>> If I printed $900 and loaned it out, I'd be arrested.

The bank didn't print one damn thing in your example. They loaned out money that people gave them as deposits.