While this is technically true, it is a partial description and a bit misleading.

When a loan is taken, it is usually not taken just to sit in a bank account, it is to be spent. When that happens (by cash withdraw or transfer to a different bank), a bank must release/transfer base money, which it can get from cash deposits, incoming transfers or in exchange for some other assets.

Therefore, although banks create M1 money by lending, they are limited in practice by necessity to keep balance of base money. So it is more a distributed/emergent behavior, where each bank ability to create M1 money is limited by its market share and the rate of money production by other banks.

You’re assuming the loan stays at the bank as a deposit, but normally one takes a loan to give the money to someone else. As soon as the client goes to the teller to get her money, or a cheque she wrote is cashed, or whatever, the balance sheet of the bank will change again (and shrink unless whoever gets the money deposits it again at the same bank).The asset (the loan, the fact that the client owes money to the bank) will stay. The liability (the money the bank owed to that client) will disappear, together with some of the liquidity that the bank had in its balance sheet. It’s ability to lend money has disminished and eventually it will need more liquidity and/or financing (in the form of new deposits, interbank loans, bond issuing, capital raising, central bank credit lines or whatever).

Yes, there are of course limits to bank lending. Ultimately, the limiting factor is the ability of banks to make profitable loans. The capital and the reserves will follow if the profitable loans are there.

The money lent does not go away when the check or whatever is cashed at another bank. The reserves follows the check. We're just working with more balance sheets now.

As long as the loan asset remains in the books, it earns interest which will add to bank equity.

We can keep bringing up details, but the basics remain the same. Bank lending creates money.

We agree, money (under various definitions) is created within limits.

In fact banks also create money when they take cash deposits (and destroy money when they hand out cash).

If I deposit a $100 bill into a bank we’re increasing the money supply because I have $100 and so does the bank (until it spends it, trades it for a non-money asset or lends it out).