Optically there is not so much of a drawback in using the F mount for these lenses, and Nikon has better AF for action in their current F-mount cameras. However, there are advantages such as silent high fps photography that may be realized in a future mirrorless camera.
I think Nikon will introduce Z-mount supertele primes at approximately the same time with a flagship sports camera with Z mount.
I totally agree. And I am sure ther will be at least one Z-mount lens of this type, when the (lets call it) Z9 will be released maybe even a 120-300/2,8.
Furthermore I wonder whether we see a totally new type of lens or whether it will be a parallel version (like the two 70-200/2,8) versions - either letting the SLR sports photographers in their own rights or trying to force them to switch systems if they want to use the new lens.