In an attempt to compare apples to apples I do not think that 28 1.8 is a good example. I mean the comparison must be between L lenses and L zooms or non-L lenses and non-L zooms
if you do a lot of landscape/wide-angle then I wouldn't go for primes. The comfort of being able to zoom beats shallower DOF. The zoom cannot beat the quality at the edges though. Zoom lenses are worse.
Having the said that, in the case of some of the older primes like the 28 1.8 and 20 2.8 the corner performance isn't really any better (and in some cases worse) than the zooms. I considered getting the 28 1.8 as a fast standard prime for a crop camera but was put off for that reason.
Very true..... mind you, the non-L full frame zooms are getting a bit thin on the ground these days!