Why Might a Miner Prioritize a Zero-Fee Transaction over a Low-Fee One?

A miner would almost never prioritize a zero-fee transaction over a valid low-fee one unless the low-fee transaction is invalid or somehow undesirable. The primary exception is when the zero-fee transaction is created by the miner themselves, such as for paying out pool members or consolidating funds.

In this case, paying a fee would be pointless as the miner would simply be paying the fee back to themselves. Another rare scenario is in an extremely low-traffic environment where block space is entirely non-scarce, making the opportunity cost of including a zero-fee transaction negligible.