Nothing interests me less than another average zoom lens that doesn't have a constant aperture..... If you're spending that much on a body, why compromise on a crappy lens?Why would the lack of constant aperture make a lens crappy? Are the 100-400 and 70-300L lenses crappy?
I'll chime in here, I guess it's convenience when shooting with a constant (stopped down) aperture and need some light. I don't mind an aperture range from f/3.5-4.5. You can stop that down to f/5.6 for the entire range for instance and still have a reasonably wide aperture. I usually do the same with an f/4 lens. A short zoom that ends in f/5.6 is not fun when struggling for light as that would result in f/8 to or so to get optimum sharpness especially with a cheapie.
Of course this all assumes that you need to stop down some for best sharpness as is the case with most zoom lenses. and there are a very few exceptions.
I love my 100-400 but almost always use it with apertures stopped down to f/6.3 at least.
5D3, 5D2, Sony α6000, G16 | SY14 f/2.8, Ʃ20 f/1.8, 24 f/2.8, 35 f/2, Ʃ35 f/1.4A, 50 f/1.8 I, Ʃ50 f/1.4 EX, 100L Macro, 17-40L, 24-105L, 70-200 f/2.8L IS II, 1.4x II, 2.0x III, 70-300L | E-mount: SY12 f/2, 30 f/2.8 EX DN, 16-70 ZA OSS, 55-210 OSS, Metabones SB | FT-QL, AE-1P | FD(n) & FL lenses