You just answered your own question about civilian rifles with flash suppressors. They look nice. It's like an old hood ornament before the just started working them into the grill or laying them flat in the hood. It adds a little style to it IMHO.
They add just a little weight for recoil (not a big issue with .223 but other calibers are different) or direct the muzzle blast to aid in better control. Especially, if you are shooting FA or even rapidly in semiautomatic.
Now the Double Defense with the Aimpoint is a little funny. I can MAYBE go for the red-dot BUT a regular bead or even XS big dot night sight is plenty. You could do a Speed Bead or ghost ring if you want to get fancy. IMHO that's enough for HD shotgun. To each his own on that issue. I can see the benefit of putting a SMALL bit of rail on the bottom for a flashlight on a HD weapon. If for nothing more than aesthetics, I like it better than the zip-ties or duct tape method. Nothing wrong with flat black finish. Polymer would have been better than painted wood IMHO but no big deal. Perhaps it's done to use up stocks and foregrips that have a real ugly grain pattern or don't match well. Better than scrapping them or putting them on guns that you can see the pattern. If nothing else it's cheaper to paint than finish the wood. As far as the lack of hammers on it, I say "good." You don't want to fiddle with the "rabbit ears" in the dark. Even if you're fast at it, you can still just pull the trigger faster than having to do both. The single trigger is a preference issue. It is more "natural" for a person unaccustomed to shooting double guns to have only one trigger. In a HD scenario, I don't see a concern for selecting which barrel you fire first at a bad guy. Now if the 1st shell doesn't fire, it would be nice to have the 2nd trigger because IIRC the second barrel won't shoot until the first one is shot. (Please correct me if I am mistaken.) Lastly, I don't know for certain if this model has extractors or ejectors. Most coach guns have extractors instead of ejectors because SASS doesn't allow ejectors. Ejectors would be preferred for HD shotguns and since this gun isn't SASS legal, I see no reason not to have them.
I think the concept is very good. It's a "point and shoot" shotgun for a specific purpose. Very simple to operate. I think the target market is "non-gun people" who want something around the house for protection. I'll keep my 870 but the Double Defense has a purpose for certain.
The Mossbergs with the phallic muzzle breaks are (IMHO) way goofier looking than the Double Defense. Especially when mounted on a pistol grip only model. If you're shooting something that stout to require such a muzzle break, you better shoulder that thing.
I can only hope the Mosin Nagant was done as a joke. It probably wasn't though.