What makes you think it would be much cheaper? I think it might have to be more expensive. The anonymity aspects of bitcoin could result in more fraudsters getting away with fraud.
But the CC system also provides anonymity, since most cards used for fraud are stolen anyway, so the fact they're tied to a real person is irrelevant.
Bitcoin, on the other hand, doesn't suffer from the same problem as CC - that the payment info must be shared with every single merchant - so it's potentially must harder to steal; Target wouldn't have a copy of your bitcoin wallet just because you bought something from them, for example.
Ignorance creates comments like this. Bitcoin transactions are not reversible, you have zero opportunity for fraud as a buyer.