About my experience on the Tokina, I usually shoot landscape at F8-F16.
The only times that I have shot this lens @ 2.8 was during an event indoors where I didn't want to use any flash.
So far, it has performed very well.
Yes, the 2.8 is a plus factor on this lens.
For landscape, you "may not" use it (F2.8) but there is a saying " it's better to have it and not need it, than need it and not have it"