I really don't see credit card processors using crypto currencies ever. Bitcoin was designed to make it cheaper then using something like a credit card. If someone were to use a credit card to transact with bitcoin then they would lose the advantages of using bitcoin in the first place.
They might, if we ever get to the point (many years into the future) where fiat becomes obsolete. The advantage of credit cards is, at least in part, for people living paycheck to paycheck, they can spend money that they don't have yet and pay the bill later when they've been paid. But I agree with your overall point, it does seem rather counter-intuitive that someone would use both a credit card and bitcoins at the same time. Debit cards would make more sense, though.
Debit cards would make even less sense then credit cards as they have the same costs as credit cards but would not have your counter point as above.
I doubt that any crypto would ever be so widely used that fiat would become obsolete as it is near impossible to garnish bitcoin from someone. Today for example if you were to spend $5,000 with your credit card, then simply don't pay your credit card bill despite having the ability to do so and have say $10,000 in your bank account then the credit card company can get a judgment against you and the court can order your bank to give the credit card company the $5,000 that you owe out of your account via a garnishment. This would simply not be possible with bitcoin.