As many may know 2 stroke engines do not have positive lubrication of the piston, crank and big/little end bearings. They have to survive on an oil 'mist' delivered by the fuel/oil mixture induction through the crankcase. This means good 2 stroke oil, if anything, needs inherently superior lubrication qualities to the 4 stroke stuff, plus it also has to mix easily and fully with the fuel and leave minimal ash deposits behind when burnt. A different set of requirements to 4 stroke. 2 stroke oil in a 4 stroke will obviuosly offer very good lubrication initially but it is not formulated for long sump life and would degrade quickly IMO. The viscosity of 2 stroke is also formulated for cold delivery so what is the viscisity going to be when hot? As for using 4 stroke oil in a 2 stroke, again it will work to a degree but a lawnmower or hedgtrimmer is one thing and would you really want to risk it in a relatively high performance (and expensive) motorcycle engine??
2 stroke engines are still being made for numerous applications but are being phased out for road use, due mainly to ever tightening emmision laws. 2 stroke outboards are now illegal in many countries. Interestingly, at the cutting edge of performance 2 stroke technology in the world 500cc GP's (now MotoGP 4 strokes) the big 4 Japanese manufacturers reckoned the 2 stroke was nearing the end of it's development with the 500's kicking out over 400 bhp/litre so that coupled with the drive for cleaner emmisions was the nail in their coffin.