But if that were a viable solution I think you'd see it being done. You don't in my experience. At least not a major sporting events, press events or Paris runway shows where rapid fire flash is de rigueur. You do see Nikon SB-910, SB-5000, Canon's 600 EX RT speedlights powered by Bolt external batteries and the like. The last runway show I was at I saw quite a few Profoto A1s and now the A1X.
The Nikon SB-5000 is rated for 100 continuous flashes and is going to need to cool down before you fire it again. The Canon is close to that level of continuous use without burning up.
I'm using the Profoto B10 which will give bursts of 20 without a misfire or change in output/color temp.. It's not on camera, but on a compact stand beside me or in the hands of an assistant. That's the most compact option that's viable. If I need more power or faster recycle then I use the Broncolor Siros 800L or the Broncolor Move if space isn't limited to a monoblock.
I've seen it done with wildlife. It was a small studio flash (bigger than an AD200, but smaller than a full-size unit) attached to a video cage on a camera, with a cable to a portable battery pack on the shooter's belt. Reflector was a custom CNC job, with a high-polish inside and a Fresnel lens attached to the front (not sure whether this was off-the-rack, taken from another non-photographic device or another CNC job). She was using it in short bursts at high speed, probably 10-15fps for 1-2 seconds at a time, as fill flash, shooting birds with a long lens on a monopod. Considering the size and weight of the setup, it actually didn't seem too unwieldy.
I'm hoping to achieve the same thing using the AD200, without having to resort to custom CNC-produced parts. At the moment, it looks like precisely aligning the flash along the axis of the lens might be the hardest part. Speedlights do this automatically - just put it in the hotshoe, set it to point straight forward and it will stay there. It would be easy enough to do in a controlled setting, aiming at a wall and making gradual adjustments until the flash hits the centre of the frame, but much harder for a flash that needs to quickly come on and off the frame in the field.
I've also heard of photographers using AD200 and AD360 units on-camera (well, technically off-camera, but attached to the same frame as the camera) in the field for wildlife, although usually for more reach or direct illumination than for rapid-fire fill flash.
There's no reason to do it for sports or fashion. Distances in fashion and press events are shorter, so high flash power is less necessary, while sports photographers can often set up much more powerful off-camera flash units on ceiling or other out-of-the-way mounts - the tennis or basketball court isn't moving anywhere. Getting rapid-fire, high-power fill flash at faster than the camera sync speed would appear to be a unique wildlife photography challenge.
Incidentally, it looks like you can mount a Profoto B10 on-camera if you want:
https://www.promediagear.com/BBX-BOOMERANG-FLASH-BRACKET-For-Weddings-and-Portraits-for-Canon-Nikon-Sony-Pentax-Olympus_p_196.html. I can't find a flash extender that works with round flash heads, though, or an off-the-shelf reflector that narrows a bare bulb's light output into a 10-degree-or-less beam for long telephoto use, so have limited interest in them for this purpose.