I clean the bar off the floor then I do my reps. I understand many are thinking it's only a delt exercise but think systemic. The whole body has to balance and stabilize the bar when you are standing. You don't realize it but you legs, lower back, all your various ab muscles and many others are at play when you are doing a standing press.
Think of it this way. Do you think isolating each body part seated in a machine will make you a better athlete? I think you can be build a better athlete by doing stuff like the clean and press, squats,chins, dips and power cleans. Sometimes you have to think outside of the bodybuilding box and think what will make a better athlete.