Eggs are probably "mostly fine" to be honest. Most homes could easily raise their own chickens and have a nearly unlimited supply.

As a prepper and a homesteader (amateur/beginner), I realize that low carb and high fat/meat isn't really feasible when SHTF, and I mostly stock lentils, pintos, rice, wheat, quinoa, and a few other standard staples. They stay good, when properly sealed for like 25 years (quinoa only 8 years or so though...). No meat known to man (or at least myself) does that. Also, even doing basic homesteading, you tend to eat more veggies and much less meat.

In the meantime, I admit that I eat plenty of meat, and could probably raise a cow or some pigs, or at the very least do the rabbit thing, but it's a lot of work and planning, and it's just easier to get your meat from a can in an emergency situation.

Edit: I prep for emergencies, FWIW, not health. Calories and nutrition are the major requirements.