Per one bike history I have read there was one quite efficient shaft drive done in the late 1890s, the Waltham Orient as I recall. Rather than standard bevel gears it used some form of rollers for the gear teeth.
Several track speed records were set with this bike while being ridden by Major Taylor per what I read. That would indicate high efficiency it appears.
I believe the major problem with current shaft drive bikes is poor design on the shaft drive itself per posts in a recent thread here on Dynamic Bicycles shaft drive bike problems. They just do not stand up to agressive riding, even without the question of efficiency. Hub gear failures were also mentioned so they may have too low an input ratio to the gear hub.
Any member have a link to info and drawings of the roller drive bvel gear arrangement used in the Waltham Orient?