[majormajor]

I think you're making a different point than the original article. Yes, retail banks operate in an economically profitable way. But that's not to say that branches are required. There are retail banks without any branches. They can still do all the lending you mention. The author is attempting to answer the question of why those haven't put the ones that spend money on branches out of business. He also alludes at a followup around "semi-public infrastructure deployed as commercial real estate projects which are funded by private capital."

However: "Instead they are required to keep at most 3% of depositor funds on—hand while they loan out the other 97% at a very profitable spread between interest charged on loans and interest paid to depositors."

So if you bring in $1000 a 3% requirement means $30, and you can lend $970. Where do you get $97,000? Say the bank wants to loan money to home purchasers. "Numbers added in a bank computer" aren't gonna pay the bills for the people on the other side of those home purchases who are going to want cash or money in their own bank, not just yours.

Are you assuming a recursive process? Lend $970, have it redeposited by the person the borrower pays, lend out another $940, etc? But that only works if the money keeps getting redeposited at which point it's not entirely fair to characterize that as the "original" deposit only, and my understanding is that that's the (somewhat hypothetical) "money multiplier" which I've always seen as 1/r which would be 33x for 3% not 97x anyway. And in practice, that doesn't get reached.