I have a tapered bottom bracket on my bike, like the one in the pic. On this bike, as I bought it, the fixed cup is on the drive side of the bike, while the adjustable cup is on the non-drive side. In order to accommodate the derailleur mech, the fixed cup is not done up flush with the frame, and actually sticks out a few mm. If I adjust the BB so that the fixed cup is flush, the gears can no longer be made to work, so this extra length has to be in place on the drive side, but with this being the fixed cup with no locking ring, it's hard to get it to stay properly tightened.
My question is, is there a good reason the fixed cup is on the drive side, or is there nothing stopping me from swapping the cups around, having the fixed cup flush on the non-drive side and letting the adjustable cup offer up the extra distance on the drive side?