Glockfan,
No military shotgun that I ever saw(or heard of) had a sidesaddle. I carried them for 20 years in the military and 20 more as an LEO, then went back as a LE/Security trainer. The reason is that attaching ANYTHING to the receiver is not a good idea, particularly if it "squeezes" the receiver with screws. Even a steel receiver can be squished that way, at least enough to malfunction.
Outside of being "tacticacool" most of the hang ons are not really useful. The only accessories I have ever seen a pro have on his SG are a butt cuff, and possibly a light(I have mixed emotions about a light). There are some advantages to an optic, if you are going to use slugs. Outside of that, ghost rings are about as esoteric as you want to get.
I have a tactical/military SG collection, I have 2 with sidesaddles, one came with it on, the other I put on to see if I could get the gun to malfunction-I could.
You will hear some people say that a butt cuff will affect the operation of a semi auto SG, particularly a short or long recoil gun-NOT! What will cause a problem is not shouldering the weapon properly, or limp wristing it if you fire from the hip.
BTW, having a pistol grip on a SG is worse than useless. A folding stock is really for carrying in close confines(aircraft or vehicle) to be extended and shouldered ASAP after disembarking. Full length stocks with PG also put you at a disadvantage if you have a close confrontation, like having to use it as a striking weapon,(some of us remember the vertical butt stroke). If you do have to retain your weapon or use it as a striking weapon, a standard stock is best, as it puts both of your hands in the same plane, making disarming you much more diffifult, and your striking much easier. After all, a SG is a short range weapon, right?
The Marines are just discovering this with the new Benelli, not a bad SG, but a really bad striking weapon.
OK, EOR (end of rant).