> the statement "banks lend out reserves" is demonstrably wrong.

It is indeed wrong, but nobody here has made such a statement. Saying "banks lend out reserves" implies that when a bank issues a loan worth $X, their reserves are immediately reduced by $X. I've been pretty clear in my statements that their reserves are not reduced until the customer withdraws $X to another bank (which does not always happen, and even when it does happen, other customers from other banks transfer funds back into this bank, so the net flow is not always negative as multiple banks keep issuing loans and money is shuffled between banks).

> banks aren't constrained by their deposits, but rather their capital which can take many forms

Sure! I like this way of putting it.

Now, a bank which has a high amount of capital can in practice issue more loans than a bank which has a low amount of capital. And one way of increasing the bank's capital (and thus improving the bank's ability to issue loans) is increasing the bank's reserves. So there's some kind of positive correlation between a bank's reserves and its ability to issue loans, right? You mentioned yourself that a bank has to have sufficient capital to survive short term liquidity events, and issuing a large amount of loans increases the probability of such events.

> I've provided reference documentation from the RBA (that's Australia's central bank) and APRA (Australia's financial regulator), and the original paper is a document produced by BoE which is the UKs central bank, so I think this is a little more than a purely theoretical argument!

The sources you've provided describe the "general case" of banks making loans as part of normal business proceedings. The documents do not describe the extreme case of a bank issuing infinite money to the chairman's wife. I don't believe that the writers had this extreme case in mind at all when they were writing these papers. You're making the argument that the same mechanisms that enable the general case would equally apply to the extreme case. I don't believe that, and I don't believe all of the writers of those papers would agree with you either. Even if the writers are sometimes using inappropriately strong expressions like "there is no relationship between customer deposits and loan issuance", I don't believe they mean that literally (and if they do mean that literally, then I'm going to argue that the papers are wrong).

Let's go back to the concrete example: A bank is known to have lost ALL of its capital and is known to have billions in liabilities that it will never be able to pay off. The bank then issues a $10B loan to the chairman's wife. The chairman's wife then exchanges that $10B to physical yachts and aeroplanes. You believe that this can happen in practice, because you believe that the central bank would provide the reserves needed to settle the transfers, even though the central bank is aware that the bank is acting with malice and committing fraud. You believe that this behavior might "lead to the loss of a banking license", but you don't believe it might prevent yacht-buying and aeroplane-buying before the loss of banking license occurs? If I understood your position correctly, then we disagree here, and I'd be happy to change my position when a single counter-example is presented. If something like this has never happened in history, then I don't believe it can realistically happen in the future either.

The reason why I'm bringing up this extreme case is to demonstrate that clearly there is some connection between the bank's... I'm going to say capital... and its ability to issue loans. This connection also exists in less extreme cases, but it's easier for me to demonstrate with this extreme example.