Well, yes, if I had the financial resources to pick up a Sony 400mm f/2.8 and a 600mm f/2.8, I would have done that..... And, yes, using one of those lenses on the A9 or A9 II body and with a 2x TC one can obtain fantastic results, as I've seen on images from others who have those lenses and either the A9/A9 II or the new A1. I wouldn't use a 2x TC on my 100-400mm or my 200-600mm lenses but, both work fairly well with a 1.4x TC. A prime lens with fixed aperture throughout the focal length range does make a difference. I saw that years ago with my Nikon 300mm f/2.8 and both a 1.4x TC and a 2x TC. You're preaching to the choir here! Thing is, I do have my financial and practical limits and plonking down upwards of $12,000 for a lens is where I draw the line.... I am not a professional, nor do I aspire to become one, I just enjoy shooting what I can with the gear that I choose and can afford.
Have you actually ever used a Sony camera body and lens(es)? What makes you so certain that "Sony still has to nail down the eye focus and tracking on both video and still photos..." ??
As for how fast the burst modes are on the A9 or A9 II, I don't know off the top of my head, nor would I presume to speak about the eye focus/tracking on them, since I have not used either of those camera bodies.