The flagship bodies I have owned have been D1, D1h,D2x,D3x...and each one has been absolutely superlative in its own era. The D3x is still an amazing "shooter", in terms of how it actually works.
Let's put it this way: take the four most-critical f/2.8 professional optics Nikon makes, the 14-24, 24-70, 70-200, and 300/2.8, and put them onto a D3 or D4 series body, and then on a D610 or D810. The sheer size, and weight of the body acts as "ballast" against the mass and weight of those common pro-level lenses. Put the 300/2.8 on a monopod with a D610, and its out of balance and ungainly. Put a D3 or D4 on the back of that same lens on a monopod, and the balance is ideally matched. An un-gripped half-height body is not all that well-balanced with these heavier types of lenses, especially for long shooting sessions. And yes, for vertical shooting, the flagship bodies have the built-in trigger and controls that make it easier to grip,swing,handle, and shoot with a bigger lens like a 70-200 or 300mm f/2.8 model, or even something bigger,longer,and much heavier like 400/2.8 and so on.
Same goes for event lenses; the half-height, lightweight bodies are a *female dog* on the wrists when matched with the heavy, high-performance lenses. As in many things involving the human body, BALANCE and weight distribution are keys once the activity lasts for more than a few minutes' time span. A 24-70 on a body like a little Nikon D5300 is a wrist-fatiguing nightmare, as the torque the lens creates on the wrist is terrifically high; even though a D3 or D3 weighs substantially more overall, with the same lens, the BALANCE of the overall outfit makes it easier and more pleasant to shoot with. None of this shows up in statistical comparisons, but once you try it for yourself, it's apparent.
A good example in Canon are their 50mm and 85mm f/1.2 L lenses--they are VERY heavy and dense, and on lightweight bodies, the nose-divce effect is incredible....but on a 1D series, the balance is good. The reality is that the flagship bodies are designed to work optimally with the flagship-type lenses.