Sadly, you are not of zero value to the credit card company. Every time you use the card, they get a percentage of the sale from the retailer. They make a great deal of their profit in this way. The more you spend on the card, the more profit they make on your purchases. This filters back down to us in higher prices in the shops.
I don't know so much :-/
Handling cash, cheques, etc. costs shops money too. Cash can be forged, it can be stolen from them, so they need safes, security, secure collection of the takings, a float of change in each till, etc.
The fact that very few shops will now discount for cash, IMHO, and very few (except small businesses) worry about small CC transactions of a couple of quid or so makes me think they're actually getting their money's worth out of credit card transaction fees.
I'd also rather carry a credit card than cash. If some scumbag stole it they wouldn't get very car (not at my expense, at any rate) and they'd be traceable and more likely to get their collar felt.
Kevin