When Dad took the family from the city to visit relatives and neighbors who still lived on the mountain, every family there had at least one .22 usually a bolt action, and one shotgun usually a 12 gauge single shot break action. The guns were used to hunt game for food and to defend livestock from predators. Most were single shots, few repeating rifles, few double or repeating shotguns. You miss a game animal or predator with the first shot, they disappear into the undergrowth. Repeaters were seen as expensive high maintenance items and shooting follow up shots at disappearing game or predators was seen as a waste of ammo. My Dad did teach me to shoot with the Brown family rifle, a Marlin tube magazine bolt action that stayed at Mamaw Brown's home in the city. I remember we borrowed a Remington 24 (cousin of the Browning Semi-Automatic .22) from Uncle Lawrence at least one outing, but I was expected to hit with every single shot fired.
Protection from other people was never brought to discussion maybe because that was for adults only, but I could imagine that even today a farm house with multiple residents with single shot firearms they used as part of their livelihood - to put food on the table and keep foxes outta the hen house - would not be an easy target.
Right now I have three break action firearms: an NEF 12ga fairly new with the receiver vetted for use with rifle barrels, old Savage 94 long barrel with WWII-era Tenite plastic stock, and a M6 Scout .22/.410 survival weaon. The NEF and the Savage 94 occasionally get out to turkey shoots. The .22-.410 folds to 18" so it often goes with me to the mountain if I am taking no other firearm(s).
If the modern use of a firearm is to waste a 200 round battle pack blasting bowling pins or banging steel plates, yeah the single shot break action is not useful.
I have seen too many modern single shot break action rifles - H&R 1871 Handi-Rifles and Thompson-Centers - used by their owners for hunting or pest control, "One shot, one kill", to ever question Modern Usefulness of a Single Shot Break Action