I'm just curious... don't Greek merchants accept credit cards? If not, then why not? From the merchant's perspective they get their money in their bank right away at a small discount so what is not to like about that? Plus, it is a convenience for customers so they'll get more business.
The only "bad" thing is there is a record of the sale so it makes it harder to cheat on income taxes than cash, so perhaps that is their reason for not taking credit cards? That between the CC fees and the taxes that they have to pay because they can't cheat the cost is high so they won't take them?
If so, then they deserve what they get. I personally would be very hesitant to travel with a lot of cash on my person, even in the US, not to mention a financially troubled country with high unemployment.