I'm the original poster.
A fully enclosed chain would do much the same as the shaft drive, at least as far a cleanliness goes. It's just not easy to find one except on some 3-speeds.
As for putting it on another bike, it won't work. The dropouts are really different and of course the bottom bracket has gears inside it.
I should mention that shaft drive bikes have been around for more than 100 years. I first saw one in the 1960's, a girls model Pierce bicycle from about 1900: spring forks, wooden rims, the shaft running inside the left chainstay. Very elegant, nothing as neat is made today. Of course it was one speed. Pierce went on to develop the Pierce Arrow motorcar, the BMW of its day.
M Riley