For standard gauge you can either have a 150 type carriage (wider than units like 156 but 20m in length) or a 156 (longer than 150 carriages but narrower than a 156.)
Well that clears everything up, thanks for the elegant explanation...
As a mere passenger, why on earth did the 165s and 166s get built to a non-standard size in the first place?
Historically the Western Region has had a wider
loading gauge than the other regions. Of course the track gauge in terms of the distance between the rails is identical at 4' 8.5" or 1435 mm, but the actual size of the vehicles that can operate is a little larger.
This goes back a very long way into the past, and I suspect may even be a hangover from Brunel's doomed broad gauge of 7' 0.25". Great Western steam locomotives were built to take advantage of the wider loading gauge, with large outside cylinders at the front end which were (and indeed still are on the rare occasions when Network Rail gauging engineers make a mistake in clearing the route for a steam charter) infamous for clipping platforms.
The
HST▸ fleet is more or less "go everywhere", since it was designed by
BR▸ to operate all over the country it conforms to a fairly standard loading gauge for rolling stock. However the 165/166 fleet was designed by BR for operation solely within the confines of the WR, and therefore it makes sense to take advantage of the more generous loading gauge to give a bit more space internally. Having said that, northwesterntrains' assertion that this is required for 3+2 seating is nonsense, as there are high-density suburban units operating all over the network that have 3+2 seating and aren't built to the WR loading gauge (450s are just one example).
Frankly this whole thread is a bit of a ridiculous storm in a teacup - although
CDF» -PMH may not currently be fully cleared for Turbo operation, significant portions of it are already, and the modifications that would be necessary to allow the entire route to be cleared may well be fairly trivial in most cases - as vacman said, adjusting platform edges or repositioning ground signals here and there, for example.