Q. Why would you want to lug around a shotgun?
A. A classic bank robbing shotgun doesn't take much lugging. I'd want one for close quarters, where the length of a Lee Enfield No.4 could be a significant disadvantage. Also for situations where a position I was detailed to defend was in danger of being rushed - take it out and place it handy so that when I've fired my 11 shots, if I'm about to be bayoneted before I can reload, I have 2 persuasive arguments. Plus, loaded with rock salt & rice, it would be very good for prisoner taking raids.
Q. Where would you get it?
A. Wearing a uniform does not make soldiers law abiding citizens. In fact, back in the days when a Magistrate's Court was called a "Police Court" and the only chance of a "not guilty" verdict was if a copper had recently offended the magistrate, it was common for the 'defendant' to be offered the army as an alternative to jail. It was also much more common for townies to go poaching than it is now - Tis my delight on a Friday night... to get the hacksaw out of the shed.
Q. Where would you get the ammo?
A. I refer you to the above answer, but also consider that those at home are generally well disposed towards serving soldiers, but back in WW2 far more so, because, for most people, the conflict was morally & politically unambiguous, since the threat was of occupation by a foreign power. What's a box 12g 00 buckshot for Mrs. Jones' eldest about to be shipped off who knows where?
Q. Why would you want to lug around all that extra weight and use up space in your pack?
For the same reasons our modern soldiers dump plenty of their issue kit so they can carry more 5.56mm ammo now - you can survive being hungry, dirty, and cold a lot better than you can survive taking a knife to a gunfight.