The toy model is the idea that a bank gets deposit from one customer and loans it to another. This is not how it works. If you go to a bank for a loan, they do a risk assessment of you, and then make some marks on a ledger. As a result of this, new money appears in your account.

But - what stops banks from creating infinite money? There is a byzantine system of rules laid out by the Basel Accords and national regulators within that. That system limits the activities a bank can conduct, lays out rules for the way it must go about business it can conduct, and sets capital requirements.

There is nothing close to a full reserve and the system is not defined in those terms. Rather, there are ratios. If you have so many AAA rated treasuries posted with your central bank, then you can grow your balance sheet by X. But for B rated investments, you can only grow your balance sheet by Y. When a commercial bank issues a loan, it literally creates money.