You're missing my point. I'm not arguing that the loan defaults are independent of the bank failures; obviously they're not.
I'm arguing that the loan defaults, and the consequent bank failures, by themselves don't cause money to disappear. For money to disappear, the defaulted loans have to be written off, instead of restructured. If they're only restructured--i.e., the borrower negotiates a new payment plan with the new lender (whoever takes over the bank's assets when the bank fails)--then the money doesn't disappear. And, as I said, since the borrower's inability to pay is only temporary, caused by an external event, I expect most of the loans to be restructured, not written off.
That depends on the bank's cash flow position and their reserve assets. It's quite possible that the bank might not be able to sustain, say, a couple of months of loans not being repaid even if the loans are ultimately going to be restructured.
Of course, one obvious way to forestall this would be to extend short-term credit to the bank itself. IIRC this was done during the 2008 crisis. I have not seen talk yet of that being done now, but I would not be surprised if it were.
So, you're right, but I think my overall point still stands.