Fact is, a small kit of primes will likely take up at least as much space as a single zoom--and probably weigh more. You should shoot whichever you enjoy shooting the most. This is a hobby that can be directed at stress relief and hedonistic pleasure. It need not be a stictly logical choice--resolution, price, weight, shooting style etc. Many of us in this forum shoot the lenses we have the most fun shooting and only you can make that decision.
As to ultrawide in the realm of landscape work...it would be tough to argue that anyone other than Mark and David Meunch are the top landscape photographers of our time. Yes, that's partly because they've focused on national icons, national parks etc. But those two have produced several dozen coffee table books with stunning landscape images. And the vast majority of their best images are super wide shots with an exaggerated foreground element (not a style I particulaly like to shoot, but that's what's popular).
Many or even most of us amateurs shoot landscape shots that look alike, but not like the Meunch's--just look at the images in the photo section of this forum, or on my website or whereever--most don't have an interesting foreground, or even a close foreground. Actually, most--including my own--appear to have been taken over the rail of a viewing platform. I know that's not what we all do, but it's how many of our images appear.
The "intimate landscape" ala Elliot Porter has been less in favor--at least in American print media--the past 25 years, in favor of the Meunchlike "grand landscape" shot with ultra wides. If you doubt this, look at the front cover of your local telephone book for the past 25 years--probably grand landscapes (or grand cityscapes as the case may be). Your own shooting style will dictate how to approach this. Killer Porteresque images can be made with a macro lens rather than any of the lenses we all tend to think of as landscape lenses.
My longwinded recommendation...get a quality superwide (either prime or zoom) and get a quality macro lens. Then you can cover most landscape shooting opportunities you encounter. And do yourself a favor, don't shoot over the rail at the scenic overlook! Well ok, sometimes...