Are “zero-bag fares” really profitable for airlines?
That's mostly a marketing ploy; people that don't have any bags are more likely to go with a airline that has a no-bag fare.

However not having any checked-in luggage means less overhead in terms of baggage handling as it's a bag less to load and keep track of. It also means that if you got lost and didn't make it to the gate in time they don't have to offload any luggage but can simply pushback as soon as the gate closes.

The freed-up space is then available for non-passenger cargo transport like mail.