Your run-of-the-mill shoe stank might not pose much of a survival threat, but trench foot certainly will; baking soda is great at absorbing the moisture that might otherwise literally cause your feet to rot off your legs. As for the health of your teeth -- it will be pretty hard to get through your day's rations of homemade jerky and hardtack without some high-quality chompers. And you certainly don't want to rely on that pesky fluoride that will "kill your brain over time" (um, what?).
Before they were pets, dogs were workers. They can carry their own supplies without complaint (already making them superior to most humans right now), sniff out food and water, and search for and bring down prey. Some breeds, such as huskies, have been specifically tailored to bust their butts on the barest of rations. Dogs also have a long and storied history of offensive and defensive combat use, making them perfectly suited to attack anyone who thinks they have more of a right to that sweet, sweet snack cake stockpile than you do. Which is to say, your four-legged pal is just a few training sessions and a kickass set of armor away from leading you to your rightful place as God Of The Ragged Desert/Water People.
With the world seeming to become a more volatile and dangerous place with every encroaching year, it can be hard to know exactly where you can feel safe. The modern media is overloaded with stories about violence, crime, and sensational pieces on the worst people in our society. But there have to be some places within the United States where the chances of anything like that happening to you is next to impossible, right?