As with any photography, there are often compromises to be made. I usually try to avoid f/22 on full frame, unless I really need the DoF (or I want to lower the shutterspeed) and am willing to sacrifice overall sharpness to get it, as overall loss of sharpness is often less noticeable than part sharp and part soft. With a natively sharp lens (like the 24L MkII), the effects of DLA results in less softness, so it may still be sharper than a lesser lens is at f/16 anyway (I have noticed this in comparison with the 24-105). I don't really notice any major problems at f/16 on either my 5D MkII or MkIII, but on the 7D the decreased sharpness is definitely noticeable. If I could get enough DoF at f/11, I'd use it, but for the type of landscapes in my area, it is rarely possible. It really depends on whether anything is blocking infinity or not, but you can get away with more at 24mm.
While DLA (which involves pixel densities and Airey discs, as well as light diffraction) may start around f/10 (or whatever the exact figure is) for the 5D MkII/III, but as the TDP article states, that doesn't preclude using narrower apertures and it is much lower before it becomes usable. What they don't state however, is that lens quality will also come into play, IQ on a higher quality lens will have to degrade much more before it is unusable than a lesser quality lens.