Prior to IOER, banks needed to lend money on the fed funds market to earn interest on any excess reserves. Doing so exposed them to the credit risk of their counterparty. Once it became possible to earn IOER risk free, banks had no incentive to expose themselves to the credit risk. Since banks (of all sizes) could not then rely on being able to access the fed funds market for liquidity, it became necessary for them to keep more reserves at the Fed. Perversely, as the quantity of reserves held at the Fed increased, interbank lending decreased (for more detail, see [0] pages 33-39).
> It does seem like the spread between fed funds and IOER is generally just a few bp
Until recently, it looks like the spread has been roughly 5-17bps [1]. For a floor system, it seems rather odd that this would exist at all, especially for a period of a decade (see [0] pages 18-19).
[0] https://www.cato.org/sites/cato.org/files/pubs/pdf/working-p...