Personally, I start all my saxes to the right, and encourage them to stay there always during concert and only move to center during marching and here's my reasoning:
1. If you look at the instrument straight on, you will notice a tilt on the bell compared to the keys. This is designed so that the bell is straight forward when hanging off the right side of the player's body.
2. The keys are also designed to be used on the right side. If you are starting beginners, those hands haven't learned where everything is yet, and if they have the proper shape to their hand, everything lands correctly hanging to the side. If it's between their legs, they have to contort the right wrist in an unnatural shape to hit some of the keys, or, if they have large thighs, they may not have room to move fingers correctly.
3. It looks cooler.