That only works if you're talking about a customer buying something from an established merchant. It doesn't help at all if the merchant is unknown (and therefore has no reputation to protect), or is in fact another person and this is a person-to-person transaction.
This problem is why Bitcoin needs escrow services (which most fiat currency transactions don't need), which of course add extra work and fees on top of what should be a straightforward transaction.
> Handing over all your identity details [...] allows the merchant to steal your identity and make fraudulent charges.
Charges that the credit card company pays, not you.