I'm not surprised by the extensive use of Over/Unders for high Pheasant for two reasons. One is the torque that is a function of the SxS barrel arrangement. The gun tends to "twist" when fired. That would undoubtedly be exaggerated with the use of very heavy loads. Firing a few hundred of those over a day would certainly be tiresome, even with a heavier SxS. The O/U does away with this torque.
The second reason is wear and tear on the gun. English guns are marvels of the art with wonderful balance. But that comes at a price - durability. There is a reason why those wonderfully balanced and slim SxS barrels literally wear out with heavy shooting. Note all the "re-barreled" English shotguns on the market. How many "re-barreled" Parkers or Model 21s do you see. Add the heavy loads that they use for high Pheasant and the wear would be accelerated.