I agree with some of what you're saying IOHO, but I have to rant a little on this.
JJJ should usually be split into two categories. Koryu and Gendai styles. I.e. old and new. Old being the classical and classically influenced styles which will have less effectiveness today, but is still an important heritage in my opinoin. And new being newly founded JJ styles and the like, who in most cases use modern teaching methods, Kano's Judo and whatever form of striking suits that suits their needs. Many may argue that this isn't "real" JJ, but as mentioned with the "japanese call all grappling JJ" thing, I also have a tendency to group all JJ like techniques under the mantle of JJ and try not to create a gap between styles. Easier to keep an open mind and learn what works this way, not just what your style has chosen.
JJ is possibly one of the few styles who hasn't suffered greatly in the "style vs. style" deal. By that, I mean that despite being literally hundreds of old and new styles and many more taking the name JJ all the time because it suits their method of training, still people do not bicker over what is "the real JJ". Any JJka with some self respect will explore JJ and everything it has to offer. Feel you're missing something in your ground game? Train BJJ, be a more complete JJka. Feel you're not striking good enough? Take some Muay Thai and scoff at people saying you simply do MMA. To some (including me) JJ is your style through and through, no matter what you add to the mix.. Why? Because JJ is not just about a collection of techniques. It's the principles, the mindset, the methods and motivation of your training.
The Principle of Ju
That's the guiding principle and always will be. Kano's seiryoku zenyo for instance is the perfect example. I'm starting to make JJ sound like some cheap JKD knockoff, but if you stop to take a look, this is why many simply shrug at the Bruce Lee JKD principles, because to them, it has always been this way. This is why some people shrug at Matt Thorntons aliveness, because it has always been this way.
JJ styles are vastly different. Some focus on self defence primarily and you may find that throwing people while standing and controlling them while they are down and you're still up is your main focus. Training methods will vary from common learning, randori and situational training like some sort of odd RBSD, to styles who embrace the sport aspect to be able to go all out and really test their own fighting ability in a 1 on 1 situation.
Again... nothing prevents a JJka from doing both. And many do.
I feel there's a bit of a misnomer on the part of Japanese JJ. As JJJ commonly only refers to Koryu(old) styles who still train under the idea that someone will grab your wrist and prevent you from drawing your sword, so you need to use that to your advantage. Ideas like that has vanished and people will complain that no one grabs your wrist for anything. But should we let the knowledge and technique simply disappear because no one is walking around with swords? Will we have to rediscover it AGAIN if for some miraculous reason there's an apocalypse and society is set back to the middle ages?
Ok, exaggeration on my part. But I think of JJ as JJ, not JJJ vs. BJJ. Japanese koryu styles are the styles where all this **** comes from, so knocking it off is a bit overkill. As always the message of this site is that training methods are your O and A. And as a JJka I will choose what I feel is important for what I need to learn. After all there are like I said a plethora of styles out there, Japanese, modern, even western founded and Brazilian. Even inside the various groupings there are differences in styles.
I hate grouping JJJ, JJ, BJJ because as a JJka I would want to see it "all". (Meaning what I find interesting and useful) Because the guiding principles of all JJ are very important to me.