There was a great article a few years ago in one of the bowling magazines that actually mapped out the results of a study on the optimal entry angle into the pocket to get the most strikes. However, I'll simplify it a bit.
The reason that hitting the 1-3 pocket as a right hander is the best way to strike, as opposed to crossing over and hitting the other side of the head pin, is it gives you the most consistent results, plus it gives you the most margin of error. (If I was to try pointing the ball across to the left side of the head pin, I would be effectively guaranteed to leave a 5 pin or a 5-9 almost every single time if I missed just one board left, for example.)
Hitting the 1-3 pocket with sufficient angle sends the 3 pin into the 6 pin which then hits the 10 pin. The head pin hits the 2 pin into the 4 which hits the 7. A combination of the ball and the other pins takes out the 5, 8, and 9 pins. Watch a slow-motion video of a good, flush pocket strike. You'll see what I mean. You can also see why hitting too much of the head pin results in leaving a lot of 4 pins (and even 4-9 splits), or hitting too little of the head pin results in leaving 7 pins, 5 pins, 10 pins, or any combination thereof.