As many of us know from Badger's Mass Principle, one of the most important factors in building a bow is its mass. To make well performing bows we want them to have the least amount of mass needed to do what is asked of the bow (generally speaking since moving mass is what should be considered). A wider thinner bow will have more mass than a narrow thicker bow. Therefore we want a bow to be as thick as possible without taking set. The thickness determines how far the limbs will bend where the width determines the force. For example, if a 25# and 50# bow had the same tiller, then the width of the 50# bow would have to be double that of the 25# bow and thickness of the two would be equal.
Side tillering comes at the point in tillering where we can tell that the limbs aren't stressed (taking set), meaning thickness is optimal, so we reduce mass AND weight, by removing wood from the sides instead of the belly.
I see no reason why a certain level of thickness is NEEDED for any bow but I do believe there is an optimal thickness, being as thick as possible without taking set.
