Canon 200-400. That's really all there is to it.
I agree that the Canon 200-400 is the one of the most exciting technologically-advanced lens to come out.
However, it's not as useful as what you're making it out to be.
Yes, the new Nikon 500/600 are marginally ahead of the slightly less new Canon equivalents. In actual use, you can't tell their output apart, even on the most high-resolution bodies. But the Canon 200-400 is so far ahead of the Nikon 200-400 - doubly so with the inbuilt teleconverter effectively turning it into a 200-560mm lens - and the zoom is so useful and versatile that it swings the whole balance strongly in Canon's favour.
Again, I disagree that the range is a catch-all, as 400mm is still pretty short.
Although on an APS-C, the range of 320 - 640 sounds good, the unfortunate truth is the 200-400 lens
only has its highest marks at 200mm ... by the time you're on the long-end, 400 mm, its rez scores are at their worst, no longer comparable to a legit 400mm prime, and when you engage a 1x4x extender on it to get to 640, your results aren't nearly as good as what a simple prime + extender are.
To me, what "swings the whole balance" is Nikon's AF system being
far more accurate, under
any conditions,
plus their having better primes,
plus their having a better sensor to record everything you shoot with the first two advantages.
Literally
everything important is in the Nikon shooter's favor now: the ability to capture (AF = hugely better), the better lens to capture (slightly), the better sensor to capture (by all measures).
Sure, if you shoot birds, and birds alone, get a Nikon 800 and D500. If you shoot everything from elephants to hyenas, from close range and at a distance, you can't go wrong with a 1Dx2 and 200-400L combination. Throw in a 600 or 800mm lens for those longer shots, but the zoom will give you much more versatility.
I actually know someone who shoots bears and such, and he has the 200-400L, but mostly what he uses is the 600mm.
(He probably posts 6-8 shots with the 600mm for every 1 shot he posts with the 200-400, so it's really not as big a deal as what you're making it out to be.)
The truth is, 200-400 isn't a focal length you're going realistically to be shooting lions and hyenas with (especially since the quality diminishes at the long-end).
This is why even the Canon shooter still shoots primarily with his 600mm.
Also, as to your "theoretical suggestion" of carrying both, have you ever tried to carry a 200-400mmL (8 lb) +
another long piece of glass, like the 600mm (~ 9 lb) around all day?
Do it sometime and report back to me

If Nikon updated their 200-400, that would change everything. But they haven't done so, and don't show any sign of doing so.
I have actually been thinking about all of this myself, for a very long time.
For what I am interested in, I realized having a Nikkor 300mm + 2x extender, and 2 camera bodies, would give me greater flexibility, greater reach,
and greater quality than the 200-400 would.
The way lenses
actually work in the field is they are the biggest, and heaviest, pain to deal with. And your tripod is actually mounted to your lens, not your camera.
If you're in the same place all day, shooting from a blind, then switching from one huge lens, to another, isn't a big deal.
However, if you're suggesting to do this
while hiking, trust me, it is just not something anyone wants to do (to say nothing of
carrying the 2 huge lenses around).
It is simply easier to carry 2
camera backs around, plus an extender or two, with your fixed tele lens remaining mounted on a tripod.
It is easier to let go of your tripod (which nicely stands there, carrying the weight of the lens), take the back off, add an extender, and put the back back-on, than it is to remove the massive lens, store it safely, pull-out
another massive lens, and put it on you camera. (Try both ways, on a long hike, and you'll quickly see the light

)
Anyway, if you do the math, a 300mm on a D810 (plus 2x extender) = 300-600mm range. Quality = better than the Canon equivalent.
If you need the reach, with your tripod/lens in place, it is very easy to remove the camera, slap a D500 on, and you now have 450-900mm range, which is much more useful. And quality = better than the 7D II + 200-400.
In every instance, the Nikon shooter has the better optics, and a better sensor, than anything the the 200-400 Canon can put out, on its comparable cameras, as well as better reach.
And (with the D500) better AF as well.
And, if you can't take a sharp action photo with either the D5, 1Dx2, 1Dx, D4, or even 1D3 or D700, the problem isn't with the camera or lens.
There is truth in this.
Both systems can, and do, take great shots every day.
But we are just "splitting hairs" here, "measurebating" and theorizing in a gear section, not "admiring art" in an art section

Jack