There isn't really any reason they have to sit there and wait for you unless it's really busy and the machine is in high demand. My experience is that on a slower day they'll go off while you enter stuff.

> Is "restaurant credit-card fraud" really a thing?

The only times I've ever had my card used fraudulently in my life were after trips to the US where I used it in a restaurant. It is absolutely a thing. Do you really think no one's ever thought to skim a card they're holding on to for an indefinite amount of time away from its owner?