I have been waiting to see this and it has not come up yet so I'll jump in.
Not all drive trains are on the right side. There are a few folks around
who ride fixed gear who have them on the other side. When I asked them why
they built them like this they replied, for the most part, that they just
wanted something different. Not sure if they're still there, but in the
Fixed Gear Gallery http://www.fixedgeargallery.com/
photos of such bikes.
Tom Sanders
Lansing, Mi