What's the disadvantage of strictly using the center AF point?

I have a T2i for the moment but I am looking to purchase a 5D III at some point.

Curious as to what the 5D crowd thinks as my understanding is that many of you only trust the center AF point.......

I solely use the center AF point to ensure a focused subject and then compose my image.

Why doesn't everyone do this all the time??

On the T2i I can compose first and then play with controls to use a peripheral AF point but that takes time. More time in fact than my standard technique.

Interested in why you would compose first.

Thanks