I was assuming that you were securing the board with a single bolt through the middle. Without a piece of waste under the board, as the cutter finishes cutting the hole it will (a) score the rotary table and (b) cause the outside of the board to come loose and get torn by the cutter. Been there, done that.
That's the manual rotary table; get the CNC rotary table and your dreams will be in TechniColor
Everything you say it true. I was not attempting to give machinist lessons here, I will leave that to others. Rather, increasing awareness in case a person knew someone who did machining, as either hobbyist or pro.