Once I bought my 5D3, my 70-200 f/4L IS moved from the Birding group to the new Landscape group. It does nice work there. It still visits the birders on occasion.
200mm on FF can work for birds, but you have to get close...
EOS 1D X, EF 70-200mm f/2.8L IS II USM @ 200mm, 1/60 s, f/2.8, ISO 125
Back to the OP's point, while a 400mm prime can be used for landscapes, it's likely not ideal. I and others have mentioned using a 70-xxx or 100-400 zoom for landscape shooting, but how much of that is at the long end? For me, many are in the 70-150mm range. The 100L Macro also makes a very nice landscape lens...
EOS 1D X, EF 100mm f/2.8L Macro IS USM, 1/100 s, f/5.6, ISO 200
Great Photos , Sir, Dear Teacher.