I have thought about this also. I have a small survival rifle that is an over/under 22LR/410 shotgun with a metal folding stock, ammo storage in the stock. I suppose that makes good sense. But one point I will mention. Stealth.
If it comes to a situation where I am hunkered down, say in the possible scenario of society gone bad, then being able to go out into the woods and bring home something to eat without attracting attention or revealing to anyone in a one or two mile radius that I am there and hunting (maybe out of season, even, or in someone else's territory), then a nice quiet springer might be just the thing. In other words, stealth and evasion could end up being as important or more important than the limited firepower you could pack with a single "survival" firearm of any caliber. What was the guy's name who was successfully hiding out in the wood for so long after bombing the "A" clinic, evading the FBI and local constabulary for years? Don't think he'd have lasted that long shooting meals with a .22 LR.
In addition to the right clothes and boots, I think a multi-piece light weight fly rod with some line, hooks and a few flies, and something like the BSA Tactical .22 with a tin of Predator pellets, a small folding camp saw, a good knife, a spool of strong thin wire for snares, some experience with making dead fall traps,100 ft of paracord, a small tarp, a light weight rain poncho, a couple of Bic lighters, a compass, a water bottle, a small alcohol stove, a metal cup to boil water and cook in, a small first aid kit with some ibuprofen and a 1-week course of antibiotics (just in case) would all pretty much fit in a small day pack, and would see me through a week in the woods in most temperate climates, without anyone knowing I was there, if I needed to be stealthy about it and there weren't an all out man-hunt in progress.