In the end, I think we all agree to disagreements. We choose the lens that suits our shooting needs the most. But objectively, the new 16-35 4L IS is a sharper lens, has IS, and sells for lower price.
Objectively it also is unable to do f/2.8 at all, which is the whole point and quite significant, as well as the fact that at f/11 the sharpness is similar to the 16-35 f/2.8L II - the importance/usefulness of this should not be ignored when advising on which lens to pick
As you say it depends what you shoot and how. I bet that a LOT more people could make use of even just nearing 1 stop IS and much better CA control (especially longitudinal) and overall somewhat sharper, especially on the wider end at this UWA to WA range than need f/2.8 there. Of course some like yourself prefer the f/2.8 over all of that, but I bet for an UWA zoom, rather more make out better with the new lens. Plus the new lens is like roughly $500 or so less too.
I don't disagree with any of what you are saying. Most people probably will benefit from the improvements of the new 16-35 f/4 IS, as this lens focal length probably racks up the most sales for landscape or non-demanding "general use." The increased corner sharpness and lower price will help these two groups respectively.
On the other hand, most professionals who sell their services for cash in places they have little control of the ambience will likely benefit more from (or outright require) f/2.8. But, that group is probably a smaller percentage of the lens-buying population. If someone is paying you to do something, you don't want to be in a situation where the shot desired is not doable because your lens is not wide enough or not fast enough. Also, those who are more into shooting people indoors, even casually, will benefit more from f/2.8; a shot with obvious motion blur, high ISO noise levels, or compromised framing due to lack of a wide enough angle - all are much worse than decreased corner sharpness. Recall, f/2.8 lets in twice as much light; in many cases where you don't have the option to drop shutter speed due to motion, that extra light will actually add to increased resolution as you can use lower ISO and in turn lower (or no) resolution-reducing DNR.
Which all goes back to - the new 16-35 f/4 IS is awesome and a much needed upgrade for the 17-40 f/4, but it is most definitely not a replacement for the 16-35 f/2.8 II as some are proclaiming.
You are quite right, it's a replacement fro the 17-40 f4 L not the 16-35 f2.8 II L. Which leads many of us to think that the rumoured f2.8 replacement will cover a very different range. A 12-24mm f2.8 for example would be fun. But ultimatly, if one needs the extra stop of light and the 1 stop slower shutter speed offered by the new f4 IS version can't be made to work with the IS unit, then the f2.8 is still the best option in that situation....which I why I haven't swapped out mine.
While a 12-24mm f2.8 would be fun, for group shots, I would prefer the 16-35mm range.
I use my 16-35 f2.8 II L along side a 35L and 85IIL on three cams for my wedding work. If I chose the new f4 version, there is a huge difference in light gathering between my ultra wide and my primes. it's a bit too much for my needs, but this new f4 lens is a fantastic piece of kit and I'm sure Canon will sell bucket loads. For 80% of the full frame photographic community, this is the right lens for them.