Continuously variable aperture

My office mate and I were just talking about the sunny 16 rule, and it occurred to me, "Why don't any widely available lenses allow you to continuously vary the aperture within the mechanically available range? (or are there some that do?)"
If I'm shooting film without a light meter (or digital without a light meter for that matter, but when does that happen?), then I see obvious merits to only having sqrt(2) increments in f-number, and the nice-looking reciprocal-integer shutter speeds that fall close to sqrt(2) increments in time: It makes it easier to quickly calculate the aperture and/or shutter speed that you want in a given situation. You can reckon more quickly if you only have to deal with factors of 2 (or sqrt(2), whatever...). Also it would often be painfully slow to scroll through a "continuous" (or at least much more finely spaced) spectrum of apertures while you're shooting.

However, most cameras now have aperture priority and shutter priority modes. I don't see any reason why I shouldn't be able to dial in an f/2.718 aperture and have the camera calculate the proper shutter speed. Nor do I see why conversely I couldn't set a 0.154 second exposure time and have the calculate an appropriate aperture for me. Of course, the camera could still warn me if the "appropriate" parameters fell outside the realm of possibility for the equipment; that's what my current camera does.

I guess one short answer would be that the current level of discrete f-numbers are finely spaced enough for most purposes, and that maintaining them maintains continuity with the traditions of photography. I wondered though, does anyone (basically meaning Nathaniel 🙂 ) know of a mechanical reason why continuously variable aperture would pose any problem? I can think of only a few highly specialized situations in which this feature would actually be desirable (and that's probably why it isn't generally available), but I thought I'd throw the question out there.