I use open notes A LOT,especially when I solo. They allow for large leaps that can be very dramatic, and offer opportunities for pedal tones, too. And there are things you can do with open strings that you simply can't achieve otherwise. Say you want to outline an A7b9 or a Dmn7. What better way than to use open notes? Slap-style funk is ALL about open notes, and swinging walking lines, too. An open note to a hammered-on note further up the neck, if articulated properly in time can give walking line a special lift.
Life without open notes was pretty dull, and then I started to learn how to use them.