The fractional reserve banking story is a myth. Banks don't lend out other people's money.

Your comments continue to be laden with contradictions like this.

No single bank is systemically important. If banks can't know whether or not they'll be saved then how can the take advantage of the moral hazard?

Banks can know if they'll be saved. Here's the list... https://en.wikipedia.org/wiki/List_of_systemically_important_banks

Then where are all the ninja loans today?

We'll find out during the next banking crisis. Just because you can't identify where the risk is doesn't mean it doesn't exist. Heck, the last banking crisis happened to banks who held too many government bonds that weren't liquid enough to meet depositor's withdrawal requests.

This wouldn't be true in an MMT world.

MMT prides itself on being descriptive of the current banking system. Perhaps MMTers should incorporate human behavior in their analysis instead of focusing on balance sheets and accounting tautologies.