I don't think this is the reason, cash will always have no fees. In some senses it can have negative fees if you're not very diligent with your tax reporting *wink wink*.

Not accepting cash is probably more to do with not wanting to deal with it, not needing to trust employees with it, keeping poor people out, and preventing robbery.

Credit card companies and banks know basically squat about your purchase except in certain circumstances (buying gas or flights causes more data to follow, called L2 or L3 data), or if they work with a data enrichment provider. There is a lot of action in this space right now, but the banks are hardly equipped to handle more data even if it became available.