Likewise card companies can and do report fraud to the relevant law enforcement authorities.
Credit card fraud detection already includes a lot of sophistication. The problem with stopping it and prosecuting offenders comes mainly from the scale of fraud, the relatively low amounts involved, and the cross-border nature of the crime.
Many credit card providers, at least in the US, let their customers generate single-purpose or short-term card numbers, for when you don’t trust the merchant, or need to let someone else use your card.
If we knew in advance that someone intended to scam us we wouldn’t give them a credit card number at all. How would anyone know when to use a fake number?