Chaperone is the lone shotgun that you have to aim due to it firing a single slug rather than pellets. The big ring that shows up on your screen while you are running around is your shotguns aiming reticle. It also disappears when aiming with a shotgun because shotguns aren't meant to be precise, all you do is point in the general direction of what you want to shoot and fire. For this reason shotguns do not require as much accuracy as a sniper and therefore will never require as much skill to use as a sniper. A sniper is generally shooting at a much smaller target from further away than a shotgun so while Chaperone does require a bit more precision than a standard shotgun its still less than that of a typical sniper. In the case of your standard shotgun you have to aim to activate Rangefinder. If you're telling me that Rangefinder activates on shotguns even when you're not aiming then Bungie might need to take a look at that.

You usually need to land all pellets unless you're using a max impact shotgun at REALLY close range or a final round. You have to be precise to land all the pellets. Invective is good because by firing twice quickly you don't need as much accuracy. But that's why it's exotic. Also, zoom while ADS on ANY weapon multiplies the range. That is working as intended. Obviously it doesn't do much for shotguns but it still helps.

You don't have to be precise, just shoot at the upper portion of the victims chest and you'll get most of the pellets to hit. Even in the event that the initial shot doesn't kill them they are weak enough to the point a basic melee will finish them. ADS makes a weapon more accurate and does nothing to multiply the range. Basically damage drop off will not start sooner if you hip fire but the chances of you missing a shot does increase. In the case of Shotguns you're firing multiple projectiles in one shot, aiming or not aiming isn't going to do much to the spread of those projectiles (exception for shot package when that was in the game). The purpose of Rangefinder is to increased the distance the projectiles can travel before damage drop off starts. So if you don't have rangefinder on your shotgun you don't even need to aim it to be effective with it.