If you're running a web site with any amount of customers, you're going to want to let people manage their own subscriptions with no intervention required on your part. If you don't have a way to integrate CC payments in to your product, then you would have to do everything manually.

You still need to have a merchant account in addition to a billing service, and for that, you could just use your local bank if you wanted to. I'd imagine that an online bank would have cheaper fees since there's no brick and mortar side of the business to maintain, though.