Interesting question which was touched on some 8 years ago on my Porth Dinllaen thread, with no conclusion other than my 28xx & 47xx have the offset, but my 59xx series Hall does not. All seem to accord with the relevant drawings. I don’t have any understanding why there was an offset on some locos, and not on others, the cylinders were pretty much interchangeable, so unless the loading gauge changed (presumably becoming less restrictive) I have no idea.
as a further observation, my 52xx also has the offset.
Further info; -
Page 62 of Holcroft's "Locomotive Adventure", he talks about his early work after transfer to the DO at Swindon - he was working on a scheme to rebuild the 80 single-wheeler locos into 4-4-0's - "he (Churchward) was prepared to see the cylinder centre lines pass 3 1/2 in. above the driving centre as against 2 1/2 in. in his standard types". This was some time between 1906 when Holcroft transferred from Wolverhampton, and 1908 when they started to scrap the single-wheelers, so presumably, the "standard" was in place before 1906. This would agree with Russell above.
Reading further in the Russell book, there is an interesting reference to the County tanks - page 60 - the final ten (2241-50) of these locos did not have the 2 1/2 inch offset between the axes. These were apparently built to Lot 188 in 1912, and also had the curved drop to the front frames - which apparently was designed by Holcroft. The same change appears to be the case on the County 4-4-0's the later (1912), curved frame, versions appear to have cylinders aligned with wheels, whereas the earlier (1906) versions have an offset.
The first of the 43xx class was designed and produced in 1910, and appears to incorporate the offset - it's certainly there in all the drawings of Moguls, and of their rather larger cousin, the 47xx, in Russell's book. Holcroft merely reports that he used "a No.4 boiler and brought in all the standard parts he could" as instructed by GJC. Holcroft moved to Ashford in 1914.
So, in large-wheeled engines, the offset between the cylinder axis and driving centre was discontinued in new builds after about 1912, but remained, for everything with smaller than 6'6" wheels. Presumably, it worked, and they had all the jigs, and tooling, so perhaps a case of "why change it?"