As someone who lives in the US, and travelled to europe, one of the toughest things was that many more places only took cash than in the states. Which meant I had to carry around a lot more cash than I was used to, knowing that as a tourist I was a target for theft (and I have been stolen from multiple times while abroad). With a credit card, if it was stolen, I could cancel it immediately, and I wouldn't be responsible for purchases the thief made with it. If cash was stolen, it would just be gone.
Also, I got a better exchange rate with my credit card than with cash from a bank or ATM.
On the other hand, I really liked that I payed for meals at the table instead of giving the card to the waiter, and that listed prices included tax.
That's not to say the US system doesn't have problems, it definetely does. But I wouldn't want a cash-only system either.