I can definitely understand why some people would feel rushed, but at the same time, I can't fault anyone for wanting to do a better job for the customer, and I do think that's all the cashiers and the store are trying to do. As someone else said, they're damned if they go slow, if they go fast, whatever, and probably most people prefer fast, since a grocery store isn't typically a place you want to spend any more time than necessary.
It's definitely common where I live for them to start checking out the next customer while you're still there; I wouldn't bat an eye. But now that I think about it, it's also common for me to feel rather flustered as I try to put my card away, get all my bags and move out quickly so the next customer can come through. I just take it for granted.