I use f/18 to f/22 quite often. Sometimes, it's because there is simply a lot going on in a scene with a whole lot of depth and I just
need everything to be in focus. More often, it's because I'm trying to slow down my shutter speeds to get long exposures at waterfalls, rivers, and seashores. In those situations, sometimes using an ND filter in tandem with dropping my ISO to 100 (the native on my camera is 200) just isn't enough to slow down my shutter sufficiently.
However, with the exception of these situations, I try to stay between f/8 and f/11. And, in between, f/14 is a decent compromise between deep focus and sharpness.
On a 1:1 look, f/20 and f/22 unquestionably produce softer edges and resolve less detail than, say, f/11. Take a look at the comparison below:
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Full Image (f/11 versus f/22)
1:1 Image (f/11 versus f/22)
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The smaller viewing sizes here make it tough to realize the differences to their full degree... but it should suffice. Notice that, at reduced viewing sizes, both images seem to look almost identical.
But at 1:1 view, it is pretty clear that f/11 is producing superior detail. If I only made, for example, a 5"x7" print, then the difference between the two shots would not really even be noticeable. But the larger the print, the more the difference in sharpness will start to show.
It's a trade-off, really. With many scenes that I shoot, the limited depth-of-field offered by f/11 just wouldn't cut it... in others, it'd ultimately be poor craftsmanship to unnecessarily use a tiny aperture and sacrifice detail. But the difference is very real... and choices for the best f-stop need to be consciously assessed on a situation-by-situation basis if your goal is to get the best shot.
In situations that strike me as being borderline, I'll oftentimes take shots at two or three different f-stops (ex. f/8, f/11, f/14 or f/11, f/14, f/20) and make choices about which worked best when I can pull the RAW files up in PP, take a closer look than my live view offers, and weigh the varying sacrifices in 1:1 detail against deep focus.
EDIT: It's also worth pointing out that these photos were taken with the Nikon 18-55mm kit lens. When using my higher-quality Nikon 10-24mm (a lens so wide that it suffers from its own inherent set of issues), I've noticed that the reduction of sharpness at small apertures is still present, but not
quite as pronounced. So, based on my experiences, a higher-quality lens does make a difference... but it's impossible to dodge diffraction altogether.