To me, the biggest limitation of the shotgun is that I would have to be able to get to it for it to be of any use to me.
This is true depending on your household situation. If you have no kids, and not many daily visitors, it can be loaded and in wait out of sight somewhere. The big choice is whether to have one in the chamber ... many shotguns are NOT drop safe; the safety only blocks the trigger and not the sear, so a big jolt has set them off! This is why in my Police cruiser it was procedure to have the shotgun loaded in the mag, gun in the electric holder with an empty chamber. Many a police cruiser had an unplanned hole in the roof due to errors in judgment with a loaded chamber.
If you want it next to the bed at night with an empty chamber, one just has to put the gun in the safe or put a lock on it in the morning. The lock is to prevent the thief from shooting you if you return early ... not preventing a theft of the shotgun. If you lose one, so what, the protection it provides is worth the risk. RISK VS. BENEFIT is the way to see that scenario.
Up close OO buck make ONE BIG HOLE, with little spread in most rooms, save Bill Gates home size rooms.
This is why you have a handgun: to get you to the big bore shotgun or rifle elsewhere!!! Besides, it doesn't have to be one or the other, both can be handy to have, especially so if other family members are trained in the use of fire sticks. If you go down, the kids can defend themselves.
Depending on where you live, a long gun of some sort can be a handy and life saving device. If you live where home invasions take place, multiple suspects may be your problem, and a long gun has some advantages there, in firepower and psychologically! Some folks talk about it, but have never been in extremis moments before, and I assure you fighting for your life never works out as planned. Overwhelming odds and firepower are always welcome in such situations. Great skill sets are a major plus as well.
PRACTICE, TRAIN, AND DO IT SOME MORE!!!