It's way more convenient. In the US, primarily, you either ask for the bill, you wait until they bring it, you give them your credit card, wait for them to charge it and bring back your card and the copy to sign, then you are free to leave.

In the EU, you ask for the bill, they bring you the bill and the credit card machine, and you are charged right there at the table, where you have to sign (because you have an US Credit Card after all)

Actually it's kind of funny when you visit remote places in Europe, and the proprietors are confused because this is the first time they've rang up a US Credit card, and the machine spits out a second receipt asking them to validate the signature.