Around here, before a hurricane, the D size seems to sell out first. Not sure who is buying the C, but those are gone too. AA and AAA I have never seen sell out.
IDK if I'd diversify past AA and 18650 if I were starting from scratch, but at this point I have plenty of lights that use plenty of everything. I also have enough pens, ink, and paper to sustain anything short of a Stephen King or Isaac Asimov pace of writing novels beyond life expectancy. I doubt that is of any practical value unless stationery supply sales are outlawed. All my stock is in one location, no resupply caches. If I evacuated, I'd grab either AA lights; or, if I had time, 18650s + USB chargers + USB power banks + USB wall-warts + extra lighter socket USB adapter. I doubt the CR2016/32 keychain lights would be worth grabbing, even if those were on the shelf after the alkalines sold out.
I don't have anything at hand that uses things that aren't current or common: I'd have to look around for that HDS clicky to use CR123. I never, ever, ever liked those. Much as I loved my Surefire Aviator (where did I store THAT...), I never used it much because all I could think about was using up $2-$6 worth of primary cells in fairly short order. Still, those CR123 really could run impressive, small, incandescents. I was so averse to using them that I still have a small stock of 15+ year old Surefire and a couple of (good) discount brands. I loved the little hurricane lamp lithium shipping hack Surefire had. 12 batteries and a little 6V indicator lamp as a "flashlight". Cute. Nice piece of history for the collection.
In the 80s, yeah, it was wrong to say "CR123 cells were too odd to catch on and wouldn't be around long", as they seemed to hang on through the early LED era... so 85-05, 20 years is pretty long in general, though a blink of the AA battery's eye. We'll have to see about 18650. I didn't see those, particularly, until the mid 2010s. They might be on the way out by 2035? Who knows.
My "SHTF" prep only extends to "hurricane in NC", in which case I'll either have a house without a tree through the roof, no electricity, but most likely water and gas. So no AC or heat for two days to two weeks. I have next to no water storage, short of filling a bathtub and some gallon jugs.
Other case is there _is_ a tree through the roof, the batteries, lights, and places to sleep are probably damp. But, probably, it'll be possible to evacuate. If not, I'm not prepared.