The mechanical advantage to using a shotgun is that you get the spray, which is represented in many systems as a template, an ability to hit multiple targets, and/or a bonus to hit/damage based on proximity.
In the current incarnation, they seem like overcharged pistols.
I think they should default to functioning like a burst fire weapon, while only using 1 shell per shot. That would cover things like an adjustable choke (hitting 2 targets with a loose choke, or getting two attacks on one target with a full choke), while still allowing AR to reflect the loss of effectiveness at range.
It would also allow for slug ammo to exist. Make it SS/SA, +3 AR to all statted range intervals and the next interval becomes 3 AR, with no ability to burst fire.