In my opinion, (it's just my opinion, no data to support it) there are several reasons and concepts that contribute to the popularity.
1) the 'legos for big boys' concept: you can add anything on to the outside. I'll bet someone, somewhere has a sno-cone machine attachted to a pic-rail.
2) While any gun can be modifed to suit your desires, the AR-platform allows this to be done easily. High quality is available, low cost is available, (sometimes these concepts are exclusive, sometimes not)
3) lots of folks that served in the military were introduced to shooting with an ar platform
4) becasue of #2, the gun can be easily modified to fit you ergonomically, thus making it 'feel' better to YOU. I actually think that part of the reason it was designed the way it was, and selected accordingly was just how ergonomic the platform really is. So you have something that is already ergonomic to shoot, and then make it easily modifiable to fit ANYONE. With that alone, you have a head start on any other platform.
5) Sure, the social stuff associated with fears of another ban of some kind (I certainly bought into this concern, quite literally. :banghead
.
6) I'm mechanically inclined, and I intend that my next gun will be an AR/.308. I want to learn more about the internal workings, by 'building' my own. To me, there is an appeal to just that.
7) I like the idea of having multiple uppers for different uses.
8) It's light, and the primairy round (5.56 or .223 Rem) don't recoil very much, so it doesn't beat up the shooter to practice.
Anyway, those are some of the reasons that I see for why the AR is so popular. To me, it's a lot like a chevy 350: the most commonly made, and copied V8 ever, and it's used for all kinds of uses. You can build them cheap, or spend a fortune, you can make other stuff do the same job, but not as easily, nor as inexpensivly. Is it inherintly superior? No. The same concept could be overlayed on the computer world. (Dos-based vs. Apple/Mac) Part of it is mechanically driven, but an equally important part of the reasoning is the combination of 'aftermarket' support structure. It sees like every Tom, Dick and Harry with a CNC mill makes AR parts - not that that's a bad thing either, it's good for the consumer to have options.
The more I learn, the more I like the platform.
PE