I think this is an interesting question and I'd love to hear other peoples' takes on it.I've been thinking about this, and I guess I'll just distill this to one simple question. How can guys like @gpseymour say he sees a lot of application training with guys like @Tony Dismukes, or guys like @Tony Dismukes say he sees a lot of benefit from his training in things like ninjutsu or wing chun, or wing chun guys like @yak sao say he sees a lot of benefit from other styles.... and at the same time, be so rigid and inflexible about what can or cannot benefit training? Seems pretty inconsistent to me. To be clear, I'm not suggesting @yak sao or @Tony Dismukes have taken a rigid stance. More, I'm suggesting that you guys are already open to the idea of cross benefits, but seem to balk at the idea of less obvious carryover.
Just talking about skill acquisition below:
I'm not at all against cross training and I do believe it can have benefits for your complete martial arts package. If you want to be a well rounded martial artist then you're likely going to train in multiple arts. For the most part, outside of potential time and recovery limitations, I don't think there's much downside to cross training (at least in very different arts, say BJJ and boxing) and a lot of upsides for that goal. That's especially true for me because I want to have fun with my martial arts, get some exercise in, and get better at self defense and at this point in my life I prioritize it in about that order too. I just think that it doesn't work the way some people are claiming it does, at least for the way most people learn.
For example, I think that doing boxing and BJJ at the same time are a great way to get better at fighting in an overall sense. I do not think that doing BJJ is going to make your boxing in the ring better unless you are able to pick up skills the way only a minority of people are able to and even then I think it will be only minimally beneficial to your boxing, and vice versa. They are different enough that I doubt they'll be detrimental to each other under competition rules either.
Now if you already box and you take up Wing Chun you may also become a more well rounded fighter since you're going to get some training that boxing is completely missing in kicking at the very least. Some people, either because they are the rare-ish individual who easily learn things this way or because they work to take a piece and integrate it into what they already do (essentially make it a part of boxing), are going to find ways to use the Wing Chun to improve aspects of boxing as well. If neither of these things are true they are likely to confuse their skills and slow their progress by mixing up methods of power generation and footwork, etc.. Even if they are good at transferring motor skills between different activities they run the risk of unconsciously breaking the rules in their boxing matches if they do a lot of sparring in Wing Chun. I know that when I was studying Aikido and fencing all the time I almost threw a guy in a fencing tournament by reflex! In general I think the more you have/want to conform to a specific set of rules the less benefit you get from cross training (or at least the amount of work necessary to benefit goes up).
My own observations have taught me that cross training has a lot more challenges for most people than you'd think. I haven't taught martial arts very much but before the pandemic I owned a gym offering strictly one on one strength training instruction. We used a slow, HIT protocol that required a lot of grit but very little skill to perform well. It is much easier to learn and perform properly than pretty much anything you will learn in martial arts. I had clients that would take up some other style of weight lifting on the side, maybe because it was closer to home or they just wanted to add something else. In almost every single case it would really degrade their ability to perform our protocol properly. Sure, they could still move the weights but their speed of motion would be too fast or they'd break form and cheat to unload the weights when it got hard. The point is, they would go from having very solid form to mediocre to poor form just by adding a new type of weight lifting and that's a lot simpler than trying to integrate Tai Chi with Muay Thai. Even when people took up yoga, which is supposed to give you a better mind body connection, it screwed up their form. They usually wouldn't have too much trouble with proper form moving the weights but they'd unconsciously sync their breathing with their lifting. We used a SLOW protocol, if you sync your breathing with the movement you'll run out of breath in a hurry but even with me telling them to breath faster they wouldn't do it until it was too late.
Again, I'm not against cross training but I think that it does most people a disservice to ignore the challenges it can represent.
If you see break dancing and BJJ as being that similar I can say without a doubt you are one of the rare people who do easily apply skills that you've learned in one physical activity to another. If your brain works this way then its seems very natural that this is how things work. It doesn't work that way for most people. To them (even to me and I'm more on the "natural athlete" side of this than many) comparing break dancing to BJJ is like comparing apples to artichokes.For what it's worth, I think when you talk about playing the trumpet and playing the french horn, I think breakdancing and BJJ are about that close. Very similar. Not quite as close as breakdancing and capoira, but close.