While many players are introduced to serving with a 'bowling motion' and you can get the ball in play, this is not the ideal serving motion (nor is it a particularly familiar feeling for those who don't bowl very often). Let's see another option and why it is better.
The bowling serve is commonly taught because it clearly follows the rules of serving. But with this extreme low-to-high swing path, the tendency is for the ball to go quite high in the air. While players may want this type of serve sometimes, they may also want to use a lower serve -- especially as they advance and want to hit harder -- and this motion does not make that easy.
Additionally, the bowling serve relies only on the arm to generate speed. The arm is a relatively weak part of the body but this technique uses it almost exclusively. As players look to hit with more power, they will need to adopt a new technique that allows more of their body to get involved.
Laying Back the Wrist
Rather then having the arm and paddle create a single straight line, by laying back the wrist and creating an angle the server can more easily keep the ball low since the paddle doesn't have to go on such an extreme low-to high swing path (there must still be an upward arc, of course).
Now that the paddle doesn't have to go upward quite so much, the server can afford to hit harder. By rotating their body through the shot (like a good forehand drive or return of serve) the player can use the stronger parts of the body to generate more speed.
Players are also likely more familiar with this type of motion since they are accustomed to hitting forehands. By engaging more of the body and rather than relying mostly on the arm, 'effortless power' becomes much easier.