Dunno. The optical superiority of a 2.8 in edge sharpness is a big deal for landscapes and a lot of us shoot them wide open or quite open. If the whole view is in the distance why not shoot wide open and hand held getting the shutter speed down.
Um, not sure I agree with that.
Many modern lenses can be sharp wide open, even at 2.8 but most will have a point where they reach optimum sharpness, usually between f8 and f11. If you're shooting landscapes, much of the time you are going to want a bit more depth of field.
It is true that if you use f2.8 at the relevant hyperfocal distance you'll still end up with a fair bit in focus, but not as much and not as sharp as if you were at stopped down. F2.8 would allow you to get more light into the sensor, but with a longer lens you're going to have to keep the shutter speed up, not down in order to keep the shot steady. If you want to keep the shutter speed down for the sake of cloud/water movement in a landscape shot, you're going to be talking about exposures closer to 1second or more which is beyond what you can do handheld even with VR.
If you have a need for a 70-200 f2.8, say for events/weddings, then fair enough use that for landscapes too if you want to carry it. But if you don't have another need for f2.8, then go for the 70-200 f4.
If you happened to use the 70-200 f4L for portraits, you'd find it'd actually do alright, and the bokeh is pretty nice, but with the money you'd saved, you could easily get an 85mm f1.8 for serious portrait work.