Ten or so years ago I purchased a Dynamic Bicycles shaft drive bike with internal hub (Alfine 8) for my year-round commuting in Cleveland, OH. With a chain there, in the winter, it meant a complete cleaning at least once a week, as they use a lot of salt and sand. I tried many different lube options with chains, but with little difference in practice.
At first the shaft drive bike was great, but at about 500 miles a noise in the front gear case began, and it got progressively worse. The folks at Dynamic were very helpful, but their conclusion wasn't encouraging. At that time, at least, the front gear case only had grease in it, and they said that under high pedal loads the grease would get forced out of the gears, resulting in the noise. I am hardly a world-class pedal monster, 6' and 185 lbs, and that answer did not impress me, as someone who was such a cycler would ruin this thing in short order.
I kept the bike for a time, opening the case and re-greasing the gears whenever they started to make noise, but that ended up being almost as much work as the chain had been. For some reason I never had any problems at the hub end. They agreed to accept a return of the bike, and they told me that they were working on an oil bath system for the front gears. I was very interested in that, and volunteered to be a tester if they needed one, but I never heard anything more about that from them. However, I also never went back to their site to check.
Given the design at that time, I don't see how it could hold up to anything but light use, as there was no mechanism to move the grease back into the gears, and use would unavoidably force the grease out. From a road crud maintenance perspective, though, it was a dream. I had high hopes for it, and also looked into other shaft drive options at the time (there were two, if I recall correctly). None of those folks recommended it for what I was doing, though.
My dream commuter bike would be one with a Pinion transmission and a shaft drive, but somehow I think I shouldn't be holding my breath waiting for one to show up.