I don't put much stock in that formula. Those British "bird hunters" are usually just standing in one spot while loaded guns are handed to them. No hiking involved. And looking at the videos of those pheasant shoots, the long barreled SxS shotguns used sure look to me to be heavier than 5.5 lbs! It certainly wouldn't be much fun shooting a couple boxes of twelve gauge ammo in rapid succession with an ultralight shotgun!
I have shot lightweight shotguns enough to know they can be painful flinch-makers and don't float to the target well, especially if the fit is off a bit (e.g. wrong LOP). On the trap range it is possible to make almost any shotgun work well (though why anyone would choose to beat themselves up shooting trap with a light shotgun is beyond understanding). There the shooter has the gun mounted and plenty of time to make himself fit it before target apoears. But in the field, especially for chasing uplands, the shooter typically needs to get the gun mounted, on target, and fired very quickly. A whippy light shotgun will not be as effective, even in lighter gauges that have less recoil. There are exceptions, of course. Some people are extremely accomplished shooters and can be deadly shooting big pheasants with a 28 gauge. But there are many more people hunting ringnecks with little guns who just think they are extremely accomplished shooters. And I'm picking their shot from my birds when I clean them. I will add that being accomplished with a little gun on the clays range is still a WORLD of difference from actually hunting with one.