Fishing with a long rod and line tied to the rod tip is not new or unique (and no one is claiming otherwise). What is new to the US is the modern equipment, which allows you to fish in ways that you can't do with the cane pole you had as a kid. I know because I still have my cane pole and I've tried. Comparing a modern tenkara rod to what you had as a kid would be like comparing a modern graphite 2 weight fly rod to the cane pole you had as a kid (after adding guides and a reel seat to the cane pole). No one seems to make THAT comparison but it is EXACTLY the same thing.
A tenkara rod is a very long, very light, very fast fly rod which is designed to cast a 12 to 20' leader without any fly line at all. And if you call making 20-25' casts dapping I guess you could say it is dapping - but only if you also said that making 25' casts with a fly rod is dapping because again, it is exactly the same thing. You are using the weight of the line to propel the fly. (In tenkara it is called a "line", but it is what in fly fishing would be called a leader, whether furled or just flourocarbon leader material). Stick and a string? Well, so's your Sage, which is just a shorter stick with a heavier string.
If you can "get" the importance of drag free drifts, you ought to be able to "get" tenkara. The combination of long rod and light line allow you to keep nearly all of the line off the water so drag is minimized. Of course, having a rod that weighs 3 ounces, collapses to 20" (for walking through the woods or for travel), doesn't require an expensive reel, eliminates the necessity to mend or do a double haul or even take casting lessons may be advantage enough. Granted you can't cast past 25' but I would bet most of the fish most people actually catch are hooked within 25'.
What I don't get is why people don't get it. Not saying you have to like it, want to do it or even have any interest in it whatsoever. I don't understand why people don't understand that it absolutely is not the cane pole fishing they did as kids. No worms, no split shot, no bobbers. It is fly fishing without the reel; fly casting without the haul. And if that is truly what you did as a kid, I apologize. (But really, if that IS what you did as a kid, you ought to get it.)
Edited to add:
In order to get it, don't start from the premise that it is a cane pole. Start from the premise that it is a modern graphite fly rod. Tenkara fishing is much, MUCH, MUCH closer to fishing with a fly rod than fishing with a cane pole.
And if what you don't get is not the gear or the technique but why anyone would be interested in it, the reasons are probably as different as why different people like fly fishing. For me, I like it because with better drifts I catch more fish. I like that a small fish can still put a nice bend in the rod and a large fish feels a lot larger because of the leverage of the longer rod and because he can't take line so it is a very direct fight. With a fish of any size, you may actually need both hands to hold the rod. I like the light weight and the extreme portability of the rods. I really like that I don't even have to think about line management and never have excess line wrapped around my legs or getting underfoot (or wrapping around everything in sight when I fish from a canoe).
If what you really like about fly fishing is making beautiful 60 or 80' casts, you would not like tenkara. If what you like about fly fishing is anything other than that, you might. It is different enough from what you did as a kid, though, that you really have to try it and see for yourself.
One last point: I honestly, truly, sincerely believe that it is not getting popular because it is marketed exceptionally well. Heck, I'm one of the guys marketing it. I believe it is getting more popular because in some applications (streams under 40' wide for fish under 20" long) it really does offer significant advantages.
