Just to clarify my comment above. I mentioned using the AF-ON button allows me to recompose the scene after focusing, I actually mean small changes in composition. I still select focus points, but they don't always fall over the exact right area of the subject, when composed correctly.
My suggestion is to try using the AF-ON button for a week or two, check out the pros and cons for yourself. The majority of people, where I have suggested they try the AF-ON button, have taken to it and now prefer to use it.