Programming a CNC is really quite easy, and you can effectively have many more templates because they are not stored on a shelf, but in a computers memory. It would be very easy to generate the CNC code based on some simple parameters - length, width, corner radius and thickness. It would also give you the possibility to cut other shapes (possibility of profits from the scrap). GRBL is a CNC driver for the 328 that is the chip used in the arduino.
What you are talking would be fairly easy to implement. A limit switch would do as well as a hall effect switch - and might be easier to test and troubleshoot.
Every time the switch is hit the arduino would move a stepper motor a fixed number of steps. When the cut cycle is complete you would want another switch that when pressed would return the router to a full up position. and maybe a second push button that would let you jog the bit down to the surface at the start of the cut cycle.