Bird shot is a horrible choice, as has been stated and with a link to the whole issue given, it shouldn't even be considered. I much prefer a short barrelled AR15 type weapon for a long gun. Easier to control, faster on a second shot. Now let's take care of 2 myth's: 1) handguns, shotgun's, rifles - the db level on all 3 are in the 150's so that's not an issue, 2) with a proper self defense load the penetration is very similar to a good handgun SD round. Also, with a proper sling and training weapon retention is excellent. The only reason I see to use a shotgun over one is cost (which is a valid reason)
You are right that an SBR is more maneuverable than a full length gun, but I'd argue you are dead wrong on faster follow ups. A longer barrel reduces muzzle blast, and the longer heavier gun absorbs recoil and stabilizes the weapon during firing, making it easier to control. Properly handled, an M-16 can handle rapid fire far better than an M4 with all other parts and factors in play. Sawing off the barrel makes it easier to move around with, but it comes with a whole host of disadvantages. It may be better to move around a small area, but once you are on target, its easier to stay on target with the bigger gun, and easier to lay down effective fire.
Also, consider that the .223 loses a lot of its terminal performance as the barrel is shortened. As velocity and energy are lost, so does terminal performance. You end up firing a big blasty round that delivers only a fraction of its potential killing power. At some point, you don't have the kind of killing round you would prefer, and it will eventually be less effective. At 11 inches and less, some of the performance is that or less than a magnum handgun round, far less than the medium rifle power that 18 inches could give you, and far less likely to stop an attack in one shot. Yes, the SBR and carbines have a place in CQB, but remember it has drawbacks, it is not perfectly better than the rifle.
Besides cost, the shotgun is shot for shot more effective than the .223 in best conditions, and certainly superior against the performance of a short barrel 223. The shotgun may not have the kind of knock down power it has the movies, it does deliver a kind of shock to the body due to its heavy load weight, and has dropped people to the ground in fights. It hits the body hard enough that even the numbest and drugged up will know it hits them, and stuns those hit. Most of all, with buckshot and slugs, it can cause massive permanent damage tracks that are, well, extremely lethal and effective in stopping attackers. It may not be a super fast hydrostatic shock super bullet, but it is the example of how slow, dumb, and heavy can be effective.
The shotgun is often hand operated, not automatic, meaning it is more reliable. User error can be worse in auto loaders, if someone in the middle of the night waking up from sleep, or nervous, doesn't make sure the weapon is in battery, doesn't rack the weapon to get it into battery. In the event there isn't enough time for follow up shots, situations where only one shot can be obtained, which can take place in real life self defense for civilians, the shotgun is the hands down winner, because it is the most likely to end the fight. In the world of civilian self defense, which are not LEO or military fire fights, the lack of high capacity and quick follow ups are not as advantageous.
As for costs, not only are worthy shotguns cheaper than garbage grade combat auto loaders, SBR's require a tax stamp that costs even more. That SBR would really appreciate a suppressor, and you could be adding a lot more to the bill.
I'm not disagreeing with you completely, but I think there are serious flaws in the "only reason is cost' comment.