Could it have been so that large parts could be moved in and out?
Also, w.r.t. both the "B-W" and "BTH" batches were built new by the same company - Metropolitan Amalgamated - neither Westinghouse or Thomson Houston had any locomotive construction capability; they were the main contractors only, subcontracting actual build.
Looking through several images, I see now the centre cab "B-W" batch had double width cab doors - and the box body "BTH" batch double width doors on the LEFT hand side in direction of travel - the rebuilds are in the RIGHT hand side in direction of travel.
The rebuilds were by M-V - the sucessors to B-W - which makes it even odder.
The District Railway BoBo also had double width doors; ISTR reading one of Mr.Connor's essays on those but I don't recall anything about access for moving large internal kit; these too were actually built by Metropolitan Amalgamated, GE kit (so presumably BTH involved).
I can't seem to find an image of GN&CR 21.
Moving parts might well be the right answer, but it could equally be something else. Like was conveying small parcels _ be it OCS or commercially _ ever considered ? 120 years ago railways thought in very different ways to today.
I helped to change a compressor on this loco, by driving a forklift truck, when I worked at the Engineers Train Unit at Ruislip some years ago. And indeed the only way to get the old one out, and the new one in was via these double doors. Which was a tight fit, and the foreman went mad, when I knocked one of the door edges.