Well the rationale is that the current problem centres around massed artillery being too powerful. If you separate the effectiveness into three cannons, three artillery units will be as powerful as one current arty in terms of overall power, but in specific power, one arty will be the same as a current arty. Currently arties create a wall of death in front of them that just kills everything, so you can't fight them, if you make it so that in order to do that for one type of unit, you have to sacrifice effectiveness against all other units, it might make them a bit less unbalanced.
Arty should be anti-building/anti-turtle. Make them slow as hell and an easy kill by tanks. Would fix arty.