With a 400mm f/4 I get
I can already get 280mm (300mm) f/4 with a 70-200mm f/2.8 and 1.4X TC-14III. It is not that 300mm f/4 isn't useful, it is. It is that most of us can already get their pretty well and a separate 300mm f/4 doesn't give near what a 400mm f/4 would. And a stop or 2 of light is not insignificant.
This is the change in thinking that needs to happen. Few bought a 400mm, not because they didn't want/need it, but because it was too big, too heavy and too expensive. In 1970 we could get 300mm reasonably and if you needed more then you went really big. In 2015, we could get 400mm reasonably small, light and inexpensive. 400mm would be the new 300mm. But the camera makers can't get out of the 1970s thinking.
400mm F4 would have quite a large front element minimum 100mm, which would mean a front filter of 105/110mm. Then that large front glass would be heavy and expensive. A 5.6 would be lighter and more hand holdable. That is why I like the idea of 500mm F5.6.