A new 400 f/4 would seem to me to be a replacement for the largely unloved 400 f/4 DO, which sells for a little over $6K in the US. It would make sense to price it at somewhat more than the 300 f/2.8 IS II, but not too much more or they might lose sales to the 200-400 f/4 1.4xTC.
The 400 would likely appeal to those who need the reach, don't like the IQ of the old DO model, and can't afford the 400 f/2.8. Those who need the flexibility of a zoom and built in TC would go for the 200-400, but for ultimate IQ the 400 f/4 will most likely deliver in the way that the other recent big white updates have.
This would mean there is still a need for a 400 f/5.6 replacement, finally with IS. If they could deliver that for under $2K I would think it would be a big seller. Currently there is a huge gap between relatively affordable prosumer teles like the 300 f/4 and the cheapest serious pro models. The aging 100-400L and 400 f/5.6 are the only options if you need more than 300mm, unless you slap a 1.4xTC on the 300 (as I do). A 400 f/5.6 with the latet IS and high IQ would be a nice option, especially if used on APS-C for more reach.