No, I don't. I shoot landscapes at whatever aperture suits the photographic purpose, often including f/22. I'd use f/32 if my lenses had it, probably. (Some lenses are pretty bad stopped down that far, I don't know if it's diffraction or something else, or both.) I don't deliberately shoot at f/16 if I don't have to - clearly if I can accomplish the same goal at f/8 or f/11 I'll do that, just as with DOF. If I need to shoot wide open to yank a subject off the background, I'll do that, even if (say) an f/1.4 lens is nowhere near as sharp at f/1.4 as at f/8. (Few lenses are otherwise, but lots of people shoot wide open, don't they?) On the other hand, if the scene permits, of course I'll shoot at f/8 or f/11 to maximize the optical performance.
But don't take my word for it. Go try it! It costs almost nothing, and you'll know something for the future. It's clear that my standards are lower than the average Nikonian's, and perhaps you care more than I do.
The other thing to remember is that as long as you're not doing a sharpness shootout, you don't have someone else's f/8 (or whatever) sitting next to your print to compare against. Certainly I know of very few lenses that are poor at f/11, and not many are poor at f/16, and the ones that are poor at f/11 are poor at every other aperture too. Once you're viewing the result by itself, relative performance doesn't matter - unless of course you're in direct competition with someone else with better gear and suitably better technique. But more normally, especially for us amateurs, once you're not comparing, it's only a matter of making the image work, and that is a far easier task.
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!