Anybody here done the "Dragon Route" or "Rainbow Route"?
Not exactly, but I did go Tokyo-Kanazawa-Shirakawa-Takayama-Nagoya-Osaka, which is similar enough.
Shirakawa-go is great, and this is a good route to see it, and very easy to plan transport-wise. Go to Kanazawa from Tokyo and spend a couple of days there. Then do Shirakawa as a daytrip between Kanazawa and Takayama, and spend some days in Takayama. If you want to go from there to Osaka, it makes sense to stop in Nagoya on the way. Both Kanazawa and Takayama have enough things to do to fill a couple of days, and while they are still big tourist destinations, they're a lot less crowded than something like Kyoto.
The Rainbow Route instead seems to go directly from Kanazawa to Kyoto. Which is an option, but feels like a bit of a waste in my opinion. You can still do Shirakawa as a daytrip, but going back to Kanazawa takes just as much time as going to Takayama.
Surprisingly I also ended up liking Nagoya a lot more than I thought I would. It has this reputation online as a pretty crap city with nothing to do, but I enjoyed it more than Osaka. In a lot of ways it actually ended up being closer to what people told me Osaka is: a more down to earth, less glamourous and less touristy big city. But it is true that it lacks big, must-see attractions unless you're there during the Sumo tournament or want to see Ghibli Park.
I think the route is a bit hard to recommend to first time visitors, whose itineraries are already rushed as is covering just Tokyo-Kyoto-Osaka-Hiroshima in 1 or 2 weeks. Even if you have some extra time, there are a bunch of places on the Tokaido-Sanyo Shinkansen line that might make more sense instead (like Himeji, Kobe, Okayama, Onomichi, or jut doing more daytrips from Tokyo). But if you have a month or are doing a second trip where you still want to revisit Tokyo and Osaka, I think it's pretty nice.
I could also see it being a thing for travelers that want to avoid the crowds of Kyoto and Osaka, but ultimately Kyoto is popular for a reason.