>the bank will create the loan (an asset on their balance sheet) and a matching deposit (a liability on their balance sheet). They could do this an unlimited number of times, as long as the deposits they create are recognized and accepted by the economy.

What you're describing is a matter of accounting, I could do it too but it wouldn't create any money. The person who gets the loan usually intends to spend it in the near future, and if that was all it took for there to be a run on the banks then the system would always be in a run. The bank's ability to make good on deposits is limited by the amount of money it has in the accounts it has with other banks and the Fed, and if you trace it back, the federal reserve is the only player who is not limited by that fact.