The problem I see with going strictly with water or detergent and water is you'll have a hard time removing the scratches from miscues and chalk on the table. To remove these you have to use an abrasive. The Aramith products contain abrasives. The Restorer is courser than the Cleaner. The key is the abrasives used must be extremely fine and that break down quickly. This minimizes material removal and burnishes the surface.
Its hard to find a product that doesn't leave something behind. It may not be "wax" but something else like silicone or whatever. My sugestion is if you want them perfect is to use any of the quality plastic polishes like McGuires, Plastex, Aramith, ... then come back and remove the residue. Then for added shine (burnish) using a ball polisher that doesn't allow the balls to touch as they spin. Once you have a clean set then you can get by with just the ball polisher for a while, as long as you run them through it before they get all scratched up and dull. Like every couple hours of play.