I know that this forum has debated this before but please bear with me.

I have read that the front of the mast should be 60 inches behind the stem. Therefore I measured the three most modern boats we have (inc 2 CTs) and found 60.5, 61 and 61.5 inches.

Three people, at some time, decided that the mast should be moved backwards. Technically, why would they do that?

Is it about jib slot, weather helm, crew weight, balance or something else?

Winders provide us with the flexibility to move it forwards or backwards but what advantage is there to gain?

All of the above. 
Think of the centreboard as the fulcrum about which the boat turns so together with rake it is a matter of balance remember though the closer the mast is to this (Centrplate fully down.) the more cranky the boat will be. Like life it is a balance, and getting used to it.