While that is a nice feature bank cards almost always draw funds from your balance and it takes some period of time for the funds to be restored to the balance after fraud is detected. Whereas with a credit card I've never been out a penny for even a day the four or five times fraudulent charges have showed up on them.
I've been out a card, while on vacation, that had automatic payments for services like netflix set up on it, and used for booking the hotel, the rental car. Had to go back and change all those services, the hotel booking down at the desk, the rental car on return. Even though I wasn't out any money, I was out my main card and had to deal with a bunch of crap while on vacation. At the time, I only had the main one with a high credit limit and a secondary with a very low limit. That being said, I never use a debit card because they have all the same risks of being stolen but don't have the same consumer protection laws. I don't even carry it with me. Plus, why would I when the credit card companies practically pay me to use their card with cash back?