One of my main SHTF/prepping thoughts is that I can't anticipate all of the possibilities. And, while my "necessary" calibers are pretty much the same as yours, I can very easily see a SHTF situation where having a .22 might be useful.
Even if I don't plan to subsist off of squirrels and chipmunks, I could see the usefulness in being able to take small game when I want without blowing it full of big holes. Another thing to consider is that, post SHTF, it would be far easier to improvise a silencer for a .22 than for more powerful guns, allowing me to hunt small game without advertising my presence to others. Growing up in a rural area, it's almost hard for me to think about not having a .22 in my house.
I think it all depends on your environment. I've got 2 or 3 squirrels that hang around in my backyard. That doesn't go very far. Rural folks will have more variety, but I still don't think that there is enough game in Indiana to be much of a factor in a real "Walking Dead" type scenario.
I didn't think of the ease of silencing a .22, that is a good point.