Looks like you are correct and I'm wrong and did not see what I expected. I guess the physics principle is that the center of mass of the racket travels in a straight line with constant velocity after the restraining forces of the hand are removed and the angular momentum (rotation) around the center of mass remains constant. ...............
If the principle above is correct and the racket's center of mass travels in a straight line after the hand lets go and before wind resistance and gravity change the racket's trajectory, there are some interesting implications. (The center of mass for my racket - by balancing on my finger - is close to where the head's lower frame is on the racket's centerline.)
Toly pictures of Fuzzy Yellow Balls overhead videos showing the path of the racket's center of mass from above. The forward and side motion show well and you have to estimate the upward component.
The pictures show the racket paths from above for the three types of high level serves. With the overhead camera view, the forward and side to side motions are shown well but the racket is coming up also toward the camera and that direction does not show well, keep that 3D racket path in mind. Track the center of mass. Then
To throw the racket up - using the real high level serve's racket path as shown in the pictures - you have to release it while the center of mass is rising. Track the center of mass to see the direction that it should go on release.
1) For the slice or flat serves at the time of impact, if you release the racket rear impact when it is going mostly in the direction that the ball is traveling it should go mostly forward - and not much up or down - there should be much smaller up or down velocity depending on the exact millisecond timing when it was released and also maybe some side velocity to the right for the slice. How could you release it at around the time of impact and have it go considerably up?
2) For the kick serve the racket's center of mass has an upward velocity for a some milliseconds after impact so you probably could release it around the time of impact and it would continue with a considerable upward component.
At this point, I don't understand how to throw the racket up using the racket path for an internal shoulder rotation serve.
For a Waiter's Tray serve, the Tomahawk throw would probably allow upward release before the point of impact position of the racket. See reply # 128.