From The digital picture it looks like the 70-200 f/4 (non-IS) has better IQ than any of the other 70-200 versions except the 2.8 II.
You misread something. The f/4 non IS is good for the price, but is way down on the list.
I really preferred my 24-105mmL to my 17-40mmL, there is a reason for its low cost, it needs to be stopped down considerably for best results.
Still, if you want ultra wide, the list is limited, and the 24-105L is already weak at 24mm.
I found a low cost used 17mm prime from Tokina that I like a lot, its f/3.5 and built like a tank. They are no longer made.
Get the 70-200mm f/4 IS if you can swing it.