I have definitely had C and D cells leak. Energizer refused to pay for the destroyed Maglite because "the cells were past the expiration date", and I'd removed the cells from the device. I think the only reason I haven't seen many leaking larger cells is that I haven't used as many. As for the P-touch, my 6 AA one worked fine on eneloops. Really poor design of anything, no matter how many cells, if it can't run all the cells down to about 1 volt. There were excuses 20 years ago, but now? Switching regulator chips are far too cheap and easy to design in. Maybe there's an excuse for a smoke detector, where you'd need a quiescent drain low enough to stretch an AA, boosted to 8V, for a year or two. A relatively expensive label maker? No. Design it for 5 cells and throw in a linear regulator if you want to be that cheap. You'll still save your customer on batteries.
As for the energy density, that would hold up for a radio. For a 700mA flashlight, just as good to use a 3xAA parallel holder for D cell use. 6Ah is more than you'll get off alkaline, as I recall. And, really, is it important to be able to run your radio 4-8 times longer on one (maybe leaking) set of C or D cells, vs the 20-50 hours a few AA will give you?
What the good people of Louisiana could really use are some truly functional solar charging USB power banks. 20W+ panels that actually work, are durable, easy to use, and affordable. Also, there also aren't a great deal of functional-off-alkaline phone chargers. Panasonic makes a 4xAA to USB that's great, but 1 amp at 5V is way too much for alkalines. Better than nothing, of course. Not that the phone is all that useful in many parts of the disaster. A radio is about all that's going to get you any communications right now. The phones do have flashlights, though.
As for NiMH longevity, I have functional 2006 Eneloops, and perfectly good 2008 Eneloops. Mostly charged in the C9000. Charge terminate under 40 (or at least 45 deg), and don't cycle them hundreds of times, and NiMH lasts. Pack of 20-40 cells, a conservative 100 cycles each (200, realistically)? I call that equipped for an emergency. Sure, grab a 40 pack of alkalines for extra backup or to give to neighbors in a crisis. Get some Ultra Lithiums if it's freezing cold where you are, and your devices can handle the overvoltage (1.8x4 is past spec for many of my radios). My old emergency kit had 2 cell incandescent AA lights that probably wouldn't have made it an hour with the lithium AAs before blowing the bulb. But, sure, get a pack of those, too. For a real emergency kit, $100 on batteries is fine. I've gone way beyond that... but don't have more than a couple of gallons of water storage.