To me the choice for 20-40 vs say 16-85 is a question of priorities. The 16-85 cover significantly more range and so in many cases will be more practical, because 1 lense will do more. The max apperture is not much different and for landscapes in daylight you'll be more at f/8 anyway. They are both DC, WR, have quite modern optics.
The 16-85 will be sharper, much bigger, heavier. The DA20-40 keep contrast in difficult conditions (contra light with sun...) and is light/small. It provide the core of the most usefull focal range but no more.
If you go to Brice Canon or Zion, you can frame any kind of shoot, from extreme tele shoot to ultra wide or even fisheye. There interrest for all and also for panoramas because really you have wide panoramic view.
To me the 20-40 can be a great choice because say you want to travel light, take some great pictures and if it is not wide enough you will stich a panorama or ignore wat you can shoot and concentrate on better framing and interresting pictures in the 20-40 range. But I would say you need to know what you are doing really if you go this route.
If you don't know and want a single zoom solution that 16-85 f/3.5-5.6 to concentrate for outdoor landscape only, a 17-50 f/2.8 or 16-50 f/2.8 to also reuse the zoom for indoors events/familly shoots and a bit of portraiture or 17-70 f/2.8-4 from sigma as a compromize between all the requirements.
If you want to cqpture the whole scene you can't skip the only lens that will do that fully: a fisheye. But that's a very specialized lens with very specific rendering. Again I would say you need to know what you are doing too.
If you accept a dual lens solution, you can take one of the general zoom I speak of, even the 20-40 and add a UWA to your arsenal like a 8-16 or 12-24. The good thing of the 8-16 is that it is more extreme. it a bit like a prime. It the lens for extremes. But you'll often need to switch back to another lens. The 12-24 is less extreme but by also covering 24mm, it allows to also cover much more of common scenes/focals. That's more practical. Both solution are quite acceptable and as long you take something else to cover your other use cases, you are ok.
Whatever you choose, don't forget that you'll want to learn how to stich panorama. That a powerfull tool.
An example, of panorama, not from US but spain. That's a few DA15 shoots stiched together. Something this wide, even a 8-16 would not cover it. A fish defished would require a quite high end optics + camera to keep acceptable quality. So the best solution really was to create a panorama. You should a bit how to shoot one and see for yourself how the result looklike. Microsoft ICE 2 is free and work really well.