I'll do my best to refrain from cane-shaking and try to curtail the 'These darn kids' comments.
My responses are based on being one of those individuals professionally responsible for stopping -- or, at least, reducing -- this type of behavior.
For a quick look into how wrong these sorts of rides can go, read up on the Hollywood Stuntz event that occurred in NYC in 2013. An added bonus/disgrace in that incident -- several (now former) police officers were active participants in the ride and the resulting violence.
Why do they do it? The same reason most of us did stupid/dangerous stuff when we were young: Boredom, youthful indescretion, feelings of invincibility, immaturity, peer pressure, etc.
Why has it become so popular? Motorcycles are easy to steal (especially dirt bikes & ATVs), and they can just be dumped if necessary without much connection to the rider. Helmets (when worn) make it hard to ID who the rider was. Plates come off easily, making it difficult to track down riders. Social media makes it easy to quickly generate large gatherings. Operating in a 'herd', much as in the natural world, reduces the chances that any single rider will be caught.
Why don't the police do something about it? Barring incidents like the one referenced above, these events are primarily just an inconvenience. Police staffing levels are notoriously low these days, and many departments don't feel this is a high-enough priority to devote the resources that would be necessary to make it stop. In large part, the individuals whose personal safety is at most risk are the riders themselves. If some stuntin' wheely-boyz smear themselves across a major roadway...oh well, instant karma.
Sometimes the disruption and inconvenience rise to a point that the public demands action. When it does, I've seen some semi-effective ways of reducing the activities. For example, while many riders will remove or obscure their license plates for these rides, there are other parts of the bike that make them distinctive. One police department I know of used accumulated private and public video to develop motorcycle/rider 'profiles' (i.e. custom exhausts, special paint/sticker schemes, riding gear combinations, etc.). Those profiles were then distributed to patrol officers who would make traffic stops on the riders outside of the events. Once the riders realized they were losing their anonymity, the number of these types of rides dramatically decreased.
Great thoughts Bajakirsh.