The short answer is that interbank lending exists for many reasons besides reserve requirements, and as you can see, the market is still quite active:
https://fred.stlouisfed.org/graph/?g=138m3
While we often think of the Fed as policy-making body, it actually serves as a lot of the transactional ‘plumbing’ behind financial markets. Most US dollar wire transfers go through the Fed. When you send money from an account at Bank of America to an account at Wells Fargo, instructions are sent to the Fed to move money from BoA’s Fed account to Well’s Fargo’s Fed account. Banks need to keep large cash cushions in their Fed accounts to handle the day-to-day variability and funding requirements of operating a bank. Some days the wires you send out will outnumber the wires you receive. It will eventually even out, but in the short term you get a loan just to be safe.
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