I think Sunny 16 is a really good tool. It IS accurate. Nobody can argue that.
But at the same time - it doesn't really matter. If you have a way of shooting that works, whether it's with a meter or without - why would it matter, as long as you get what you want? And I'm a strong believer in repeatedly using the same thing, because practice makes perfect, not gadgets and gizmos, or the lack thereof.
2 years ago was kind of a photographic crisis point for me. It was either go whole hog in digital or whole hog in analog. At that point the realization came that I just hate the digital work flow. The answer was to get a mid-century folding 6x6 with zone focusing and 2 little pop-up squares to frame the scene, leaving the meter at home, and shooting entirely sunny 16 outdoors. It meant ruining a lot of film, but now I have hardly any use for a meter outdoors, and will oftentimes override the reflective meter in my 35mm. It really opened the doors to starting to understand light.
A politician is a man who will double cross that bridge when he comes to it.
I use the sunny 16 rule (or an adjusted version if it's not sunny) when I don't have a meter with me (infrequent) or I need to get a shot quickly (semi frequent). I have found it to give perfectly useable exposures with black and white negative film. In an ideal situation I would use my incident meter or a spot meter but sometimes that's not always possible. So I find sunny 16 to be very helpful. One other trick I don't think has been mentioned makes it a little easier to calculate "sunny 16" quickly with larger apertures. Add a zero to the film speed at F5.6, ie 100ISO film is 1/1000, 400ISO is 1/4000.
I only see sunny 16 as a guide point for exposure, generally don't use f16. But it's all simple math, ASA 100 = f16+1/125 or f11+1/250 or f8+1/500. If overcast f8+1/125 or f11+1/60 or f16+1/30, and so on. I call it all "sunny 16" because the starting point is ASA=shutter speed + f16 for mid day sun. If you really just stick to f16 and sunny days, then yes it is rather limiting.
I use sunny 16 as my "anchor" point. When I am working in daylight conditions, I estimate exposure using sunny 16, and then take a meter reading to either confirm it, or refine it.
“Photography is a complex and fluid medium, and its many factors are not applied in simple sequence. Rather, the process may be likened to the art of the juggler in keeping many balls in the air at one time!”
Ansel Adams, from the introduction to The Negative - The New Ansel Adams Photography Series / Book 2
Another advantage is that when you use it you begin pre-calculating exposure and using the light meter to refine it as Matt says. This has the advantage that if the ISO value is improperly set one can notice it immediately because the light meter gives values that don't fit with the mental calculation. People who shoot an entire roll and then realize the ISO was improperly set are not the people who use sunny 16.