That’s not true. It’s not just that real-world banks
don’t do that, they just plain aren’t allowed to “lend out deposits”.
I guess you could say “fractional reserve banks” do, because “fractional reserve” is a textbook model and not something that happens in the real world.
The problem is that deposits are a liability. Banks can only lever up assets to lend, so deposits are on the wrong side of the balance sheet to do that. What limits how much banks can lend is capital (and capital adequacy ratios), not deposits.
Banks create new deposits when they lend, as well as creating an equal amount of private debt. The loan is an asset of the bank, which creates a corresponding liability.
Customer deposits coming in as cash or transfers from other banks are useful as liquidity, but can never be lent.
Some details if you’re interested: https://www.bankofengland.co.uk/-/media/boe/files/quarterly-...