Question for marketing whizzes

It rarely happens, but occasionally for some reason I find I've overpaid my credit card. The card dutifully informs me of the fact of the credit, and that's it. It does not offer to send me a check. Or to pay me interest on the use of my money. I guess it assumes I'll use the card soon and kiss that dollarage goodbye. But in point of fact, the extra cash is sitting on a card I want to cancel.

So I wonder: Is there a credit card company out there that does do this -- especially, pay interest on your money? Would this not be a nice Bidnez 2.0 thing to do -- you know, like make the customer the driver of the enterprise? Or, you know, give the other end of the transaction some actual traction? Or like, evolve the credit card business into something more like banking, where one could park money and gain attractive rates of return?

You know, have an actual conversational relationship with the customer.

Just wondering.