I know a couple of people doing crossfit that are really in to it. They basically say that paleo plus heavy workouts is fitness nirvana.
Drawbacks, on the surface it looks to be an expensive way of eating to maintain, and also difficult to maintain day after day. It seems to be more suited to a person that doesn't travel, always brown bags their lunch and rarely goes to restaurants.
I agree with your comments. I work with a crossfitter that is also a paleo diet proponent. He swears by it. We had a department picnic last week and for fun I decided to make my dish to pass a paleo one so he would have more options. That was the most expensive hummus and chips I ever made! I don't think he was a fan of the hummus, but he loved the chips.
If anyone is interested in the recipes, check them out here: http://libidiny.blogspot.com/2010/08/there-have-been-many-times-since-began.html