Bully breeds obviously receive a lot of bad press, and responsible owners in general I think feel the pressure to have a well-behaved dog maybe more than the owners of other breeds (maybe)... I feel differently walking down the street with my lab mix because I don't feel the same pressure as when I walk down the street with my pit bull (even though it could just be all in my head!). But that being said, I think it makes responsible owners of pit bull breeds seek out training and those that do tend to strive for high standards, in my experience... (There are obviously exceptions to every rule and I can't generalize about what people's intentions are with their pets. I can say that in the bully world I am involved in, that is certainly the case: we try very hard to have exemplary examples of our breeds, well-trained, many compete in sports, etc., and more importantly, we - speaking for the responsible bully owners in the circles I am familiar with - strive to open the minds of others to the awesome, balanced relationship you can have with an awesome, balanced, healthy, "non-scary" pit bull-type dog.)
Obviously, these dogs are power-houses. Nobody needs to tell anybody that. We all know, and regardless of what people want to say about it, physically controlling some of these dogs on a flat collar or a harness is a challenge. That is CERTAINLY the case with many of the dogs I deal with on a regular basis... They are unruly & physically challenging to control. A prong collar can have the exact opposite effect of a flat collar or harness in that when the dog leans into it, it causes discomfort, making the dog want to back away from and relieve the pressure (in theory.. although it's possible to screw that up). Most bullies, and I'd have to say most dogs in my experience, have the opposite physical reaction when they put pressure into a flat collar... because there is no real aversive there, it tends to make the dog push AGAINST the pressure, (and it's certainly what I see on an every day basis). People get themselves into an awfully lot of trouble with powerful bully breed dogs on this principle alone.. ("Oh, he just wants to say hi!!" as their pit bull is scratching along the linoleum trying to get to the target. In the beginning, often it IS "he just wants to say hi" - however inappropriately - but months & months & years of practicing that behavior on ANY collar or harness builds up a lot of frustration, because on many of these flat collars/harnesses, applying pressure isn't enough of an aversive to get the behavior to stop. (And can frustration lead to aggression? YES.) In my opinion the use of flat collars/harnesses in this way (which can come from lack of education, not following through, or sometimes full-on laziness) can actually escalate the behavior because applying pressure to the harness or flat collar often communicates "lunge!" to the dog. The opposite effect is generally true on a prong collar.
The argument could certainly be made: "Instead of applying aversives to get the behavior to stop, why not reinforcement a behavior you DO want?" (Which I feel is completely valid.) HOWEVER, every dog is different, and different things are more or less reinforcing to any given behavior. We've all been in a situation where the dog wanted to run off more than it wanted a piece of cheese, and no amount of training with positive reinforcement is going to change that in some cases... (Imagine the hound dog who wants to chase the rabbit - and I am speaking about my first dog Caruso. I trained & trained & trained for months & months trying to do it pure positive - I was early in my career and had a more narrow view on training. I didn't want to use aversives of any kind. I was able to get to a certain point with Caruso... including stellar recall UNTIL small animals got involved. That behavior to chase was so instinctual & primal to him that is was impossible in my experience to overcome that with any amount of positive reinforcement, because chasing the rabbit was again, primal, instinctual and more rewarding than anything I could be offering. I ended up adding in correction/aversive/consequence - choose your word - for not complying with a known behavior - come when called or leave it in this example - and solved the problem. Caruso was able to be off-leash and hike with me and enjoy all the freedoms that come with reliability off-leash.)
Also, some dogs just aren't very food-motivated and all of the tricks one can use to increase their food-motivation aren't always effective to the degree that the owner needs them to be.
The bully breed dogs that we are speaking about - some dogs' drives to do a certain behavior are very, very strong, and it is not always possible or realistic to click and treat the alternative behaviors while managing, ignoring, or not exposing him to or putting him in the situations where a given behavior occurs. Applying an aversive can be an effective way to stop a given behavior faster than using positive reinforcement to reinforce the alternative... Sometimes there isn't a lot of time to get a dog to a certain point, and using aversives (including the prong collar) can expedite things. (I'm thinking about training in general, but also specifically about fosters, shelter dogs or dogs that are on their last legs - need to fix a problem in order for the dog to escape euthanasia, etc. etc.)
A lot of the dogs I work with are dogs that other people don't WANT to work with because the problems were out of their hands, or the methods they are familiar with are not making any more progress, or they legitimately feel that the best option is euthanasia. My personal experience tells me that the rates at which people come to that last conclusion are way too high, but regardless, I am often called upon to help solve problems that positive reinforcement methods alone were not working effectively enough to solve, or alleviate, might be a better word. That is where aversives in training come in, and training with a prong collar does apply the concept of aversives.. obviously.
Again, I can't speak for everyone, but the people that I interact with who use prong collars use them as a training tool because they can be used as part of a very effective training "program..." As a group, the people I know who use them are committed to training and having a well-behaved companion that enjoys all the freedoms a well-behaved dog can... I don't think prong collars are right for every dog, every individual, every time, but I don't think that about harnesses either. I think prong collars may be showing up more prevalently in pictures because they're out there... They are used a lot in the bully world I am involved in because they can be a very effective tool for training. I have some dogs that wear one, some dogs that don't. It's all about that individual dog & me and what works for us. I think people are putting the topic out there to be debated more these days, and that controversy and the die-hard support on both sides could have something to do with people unapologetically posting pictures of their dogs wearing them. That would be my thoughts on the subject of the prevalence of prong collars in dog training these days.