For these reasons, there is often less pronation or turning of the hand and racket during the upward swing. The racket can come through the shot and followthrough with the racket face pointing straight down.
This seems to be related to the direction of the shot. When the players want to hit the ball shorter with a higher bounce, typically when they are closer to the net, the motion tends to have less pronation. It may be related to the angle of the placement.
If you have a relaxed service motion, you shouldn't have to think about all this too much and it will probably happen naturally as a result of your shot choices. Note how, regardless of the pronation, the followthrough continues forward, out, and across the body in the animations.
Overall, what makes the overhead difficult is the ability to move in position with the proper turn position. The unit turn and the movement, I believe, are the two areas where the average player needs to focus. The arm swing is important, but as your serve arm swing improves in this area so will your overhead swing. As I mentioned above, conquering the ability to do the cross steps as you initiate the turn will go a long way in making the overhead the best part of your game.
The Overhead Game
There is a great live ball overhead drill that I have used many years with my high school doubles teams to work on implementing the overhead in matches.
One team is back at the baseline and one team is at the net. Your coach or one of the back players starts the point by lobbing to the net players. The lob feed should not be too tough or too easy. The net players cannot let the ball bounce either on the lob or the volleys.
The amount of pronation during the overhead varies with court position and shot placement.
After the lob is hit, the point is live. The baseline players can do anything they want -- lob, hit, go to the net, etc.
First team to five points wins, then everyone rotates (clockwise) one position and the game starts again. Rotating the positions gives the players practice from both halves of the court, which is important because of the differences in the angles.
This drill is a great way to just get completely comfortable with hitting overheads everywhere on the court. Even if you are a singles player, it gives you the repetitions and the variety of movement and positions on the court that you need.
If you haven't really developed an overhead, this game can be difficult at first because so many of the overheads are hit while moving back. Overall, though, it's the best way I know of to develop those critical cross steps. You'll know you are getting better when the team hitting the overheads starts to win the majority of the games.