There's a couple of reasons: - to separate VR activation from the focusing to conserve battery power while you compose - to combine continuous-servo and single shot mode in one set of settings. This is the most versatile setup but as your D5100 menus don't have the option to switch off AF activation from the shutter button, this technique won't work.
Personally I wouldn't use the AE-L/AF-L button for AF-On with my D5100. I do use the AF-On button extensively with my D300s but keep both AE-L buttons set the same and that's for auto exposure lock (and 'Hold' for video)
I learned the advantages of the AF-ON button when I got my D1. 1. It is faster to go from one subject to another.. 2. You do not have to have perfect touch but can mash it down. 3. You can continuously refocus when shooting a moving object. a. Focus will still lock on and track an object. b. Of course your panning skills have to be good anyway.
In response to this, I tried the AF-ON today for volleyball. It seemed to work ok. Half press of shutter doesn't focus in this mode. Only pressing the af/on button focuses for this. I had camera in AF-C. I didn't try other combos though.
I also had a few cases where the camera freaked out. I had a few images that were totally black. Info said they were at ISO 100 and f/0. Yep, f/0. Probably about 5-8 shots out of 750 came out that way. Not all the 750 were using the AF-on settings. It may have had nothing to do with settings and just some other camera/lens issue.