Blohn und Voss, in particular Dr. Richard Vogt, were convinced that an asymetrical engine/fuselage layout would solve the trim issue with propeller driven aircraft. With normal single engine aircraft, the propeller creates a torque opposite to the prop rotation, causing the aircraft to turn. Multi-engine airctaft experience the same effect if their props all turn in one direction. Aircraft like the P-38 have opposite handed props which cancel out the torque. The disadvantage to this solution is that the gearbox and propeller have to be different, which can be a minus in terms of parts suppy. The intent of the asymetrical placement of the engine is to naturally cancel out prop torque, relying on the offset weight and drag of the airframe.
Blohm und Voss apparently got it right in the Ha-141 http://www.unicraft.biz/bigph1/ha141-wilson.htm and BV-141A machines - pilots were reported to have praised their handling and aerodynamic balance at all speeds. However, changes made to the BV-141B series threw things out of balance. The horizontal stabilizer was changed to an asymetrical layout to give the rear gunner a better field of fire. The wing planform was altered to cope with the larger, heavier BMW-801 engine, which itself caused vibration problems. All of this combined to sully the handling qualities of the original aircraft.
Many years later, Burt Rutan built the one of a kind Boomerang, a light twin boom aircraft with a cabin in one of the booms, and forward swept asymetrical wings. https://en.wikipedia.org/wiki/Rutan_Boomerang The aircraft used the same priciples as the BV-141, and was (is) a successful design.
I believe the dearth of asymetical aircraft is that most people don't like weird ideas, and that tried and true conventional designs are good enough.