East is East, West is West; discuss...

As D stock is handed you couldn't turn a unit as such but two double cab units can and have coupled to form a service train as long as A and D cabs were coupled for example units formed 7500-7501+7502-7503.

Single D stock double cab units were used on the East London Line from 1985-7 to allow the A stock to undergo OPO conversion.

Well, you could - but then it wouldn't be able to couple to any other unit unless that had been turned too. The 1973 stock, which, apart from the small matter of loading guage, is technically very similar to the D stock, suffers from this problem, because it was designed before T4 was thought of). A unit can only couple to another unit if they have both been rounbd the T4 loop an odd number of times, or if both have been round it an even number of times. If there were a terminal loop on the District Line, D stock would have the same issue.

I understand a train fomed of two double-enders would be slightly too long for certain sidings.

A double-ender can operate on its own, as the trailer has two brake compressors, the minimum requirement for a train in service, to provide the redundancy required to prevent a compressor failure immobilising the train. The trailers of single-enders only need one each, as they cannot operate alone. Single-unit operation of 1973 stock was confined to the Aldwych branch and the ETT test-bed.

The east-is-east-and-west-is-west issue affects single-enders as well - if you turned a full train of D stock neither half would be able to couple to anything else.

As to why Tube cars are left-handed and right handed like this - it's simpler. Units were only designed with "Hermaphrodite" couplings when they were expected to be regularly turned in service and required to couple to units which may not have been turned the same number of times (e.g A, C, 1972, and 1992 stocks).