In my department, pulling over on the left greatly increases your chance of getting a ticket. We may write tickets to about one in eight vs. one in five that pulls to the left.
The only exception is if, for safety reasons, you cannot pull to the right. I'd rather you slow up, put on your hazards and drive two miles to an exit ramp. Cars parked next to a highway are dangerous to everyone. I don't want to get hit, I don't want the driver of the car I pulled over to get hit. The right side of most American highways has much more room to pull off further.
The drivers manuals and traffic laws all tell you the right side is best. If you pull off to the left, I'm going to assume you really need some more instruction on traffic laws. Of course none of this applies if your old, I'll usually just tell you to slow down and get you back on your way.
Point being, everyone is safer if you pull off to the right like the manual says. And remember if you get pulled over, you were speeding, I was bored and lonely, and I'm just making sure you aren't drunk with a warrant. (It gets dark out there, don't judge, lol.) So pull to the right, we'll talk for a moment, and we can all go back to what we were doing. (e.g. me watching Netflix on phone, you speeding...)