What you describe is called the “money multiplier model” and yes, it’s not how the actual economy or actual banks work.
This document [1] from the Bank of England (UK’s central bank) is the best description I know of about how those ideas (“fractional reserve”, banks lending out deposits, “money multiplier” etc.) are wrong.
This document [1] from the Bank of England (UK’s central bank) is the best description I know of about how those ideas (“fractional reserve”, banks lending out deposits, “money multiplier” etc.) are wrong.
1. https://www.bankofengland.co.uk/-/media/boe/files/quarterly-...