I'm aware of merchant transaction fees, but they're insufficient as an explanation. Just run the numbers. Say that a hypothetical consumer spends $10K/year. The person who carries that as a balance will pay $2700 at 27% interest, plus $300 from the 3% transaction fee, for a total of $3000, and they might get $200 as cashback. The person who doesn't carry a balance will pay $300 and get $200 as cashback. It's pretty doubtful that all the other services a credit card company provides - fraud detection, chargebacks, billing, recurring payments - cost < $100/year. Maybe if you never submit a chargeback and your card never gets stolen, but at best we're looking at them breaking even on their non-balance-carrying customers and making all their profits off the customers that carry a balance.

When you're providing a service to one group at or below cost and making all your profits off another group or another service, that's the definition of a cross-subsidy, even if you do get a token amount of revenue off the first group.