A reliable .22lr makes a very capable SHTF weapon.
Absolutely.
The thread seems focused on defense, but what about hunting? Let's use the scenario laid out so far. You're living on the go, having to worry about fighting off other people, and apparently carrying everything you own in a pack or even on a sled with no base camp. In this situation stalking big game will likely mean covering a lot of ground and into areas where, because you're being led by an animal, you will likely not have had time to plan an exit strategy ahead of time. You will not be able to carry all of your gear as you stalk, so this means leaving it behind in a hide of some sort. The more ground you cover, the more likely it will be for you to unintentionally cross paths with others intending to do you harm. This could land you in a defensive situation without the 100 -200 extra rounds of ammo you packed. Separated from your gear, your supplies are exposed and ripe for picking by anyone who comes along.
Even if you don't run into any bad guys and are able to take a deer, now you have added a significant amount of weight in meat to your already heavy load. Now that you have all this meat, how do you preserve it? In my mind, small game will be far more abundant and will require much less effort to take. Taking squirrel, rabbits, birds, etc. will keep you well fed without the added burden of packing or trying to preserve several extra pounds of meat. Not sure if anyone's ever shot small game with a .223 or with 00 buck but those who have, was there much left of the animal to eat? What about the sound signature? How far away can these shots be heard? To a would-be attacker, this could be like ringing a dinner bell. Parks service studies have shown that even bears and other predators have learned to follow the sound of gunshots to find a free meal.
In my mind, this is where a .22lr rifle shines in a survival situation. The number of rounds you can carry is hard to beat. It'll keep you fed without destroying your quarry and it's relatively quiet when compared to the report of a .223/556 rifle or 12ga shotgun. Contrary to the opinions of many, a .22lr rifle will serve as a suitable defensive weapon in a pinch. Is .22lr as suited for mounting a defense against multiple armed attackers as an AR-15 or a 12ga shotgun? Of course not. But let's be honest, no matter what caliber firearm you're packing, if you're alone in that situation to begin with then you're already screwed. Outside of hollywood, what are the odds of anyone realistically running into this defensive scenario? I would much rather focus on the means of staying alive when I don't have to fight off groups of armed bandits...