I thought there would also be electricity usage benefits but after looking at people online who have crunched the #s that might be negligible.
That said it makes such a small difference that it's really not worth worrying about, in fact you might lose more energy keeping the door open longer to find the thing you want in your packed fridge.
Air is a particularly poor conductor of heat, your hands touching the product to move it around is doing more damage than anything else. Your fridge thermometer only measures air temperature, not product temperature, which is what you actually should care about.