One advantage of the af-on button is that you get the ability to do AF-C and AF-S without changing any settings once you get them right: af system to af-continuous focus button (a5) to "af-on only" shutter release (a1) to "release" This is the normal continuous focus mode using af-on.
To get the normal af-c behavior, press and hold the af-on button. To mimic af-s, press and release the af-on button.
Because you have the shutter set to "release", which allows the camera to take out-of-focus pictures, you can pick any focus point, press and release the af-on button to mimic af-s, recompose (so that the focus point is not on the subject), and trip the shutter even though the chosen focus point is no longer in focus.
The down side to this is that if you don't get the subject in focus, the camera will take the out-of-focus picture.
When in true af-s mode, the a2 setting may need to be in "release" if you are doing focus-and-recompose since you will be moving the chosen focus point off the subject. (I don't recall the last time I shot in af-s mode due to af-on.)
---------+---------+---------+---------+---------+ Joseph K Seattle, WA, USA