I would think that .22 would be very useful in a doomsday scenario. I would bet almost every gun owner has at least one .22, and then after that, the calibers probably vary a lot. If nothing else, it would be a valuable trading commodity.
As the previous poster states, hunting and food gather would be the primary use, but personal defense would be a close second. I don't want to get shot with any round, centerfire or rimfire.
The amount that can be stored or carried is another consideration, because a 500 round brick of .22 probably fits in about the same space as 100 rounds of .223.
And finally, obviously prior to the scarcity and panic pricing, would be cost. It would be within the financial capabilities of many people to accumulate 10,000 or 20,000 rounds of .22 ammo, whereas that would be much more difficult for centerfire rounds. I would say now that the gap has significantly closed, as I'm seeing 50 round boxes of .22 go for $10, and there are places to get 9mm for about the same price.
Those are just my guesses/observations: I think the shortage is attributed to the gun-glut that the country has been/is going through. A lot of those guns being sold are probably .22, so naturally everybody wants to shoot if they can, which requires ammo.
Then you have people that buy it to re-sell - that accounts for a good portion. I know that one of the local gun stores' owner routinely checks Wal-Mart to see if they have any .22s which he marks up and re-sells in his store.
Then you have preppers that are stock-piling in general.
Then you have folks like me that aren't reselling, aren't shooting (much), and aren't preppers/stock pilers, but still buy our limit when it's available, simply because it is no longer always available.
I think when you add all of those things up, demand outstrips supply, at least by some portion.
These are strictly my guesses based on my perception of the situation.
Good luck and take care.