Here I am trying to awaken old brain cells to draw on memories made years ago.
A single 18650 has about the same number of watt hours, as three AA cells.
An alkaline D cell under low load, ( < 1 amp) has about the same number of watt hours, as a 3400 mah 18650.
Regarding the comparison of alkaline to LiIon chemistry, alkalines do OK under low load, but when placed under load, they fail miserably at loads greater than 1 amp.
A 3D lantern with a modern LED pushing out 100 lumens will last as well as a 3- 18650 LiIon soda can light that is also outputting 100 lumens.
IIRC the 3D alkaline light will perform fairly well up to 300 lumens, but beyond that there is no comparison to LiIons.
So I guess... primaries vs rechargeables is dependent upon the personality of the user. If the user is a flashaholic, he will likely periodically monitor the status of his battery stash and periodically top his rechargeables off. OTOH if he is one who leaves alkalines in lights long enough that they leak and cause damage, he may be better served by keeping a stash of primaries, but outside of the light.
Like Lynx_Arc, I have the ability to recharge my 18650s in my car if needed. But if the outage is that long, that I need to recharge, I'll already have my generator running to save food from spoiling.
Perhaps a blend of the two is most prudent.
Personally I rely on 18650s for the most part, but I do have about six 3D cell lanterns (yes a stupid number I know). I have a number of unopened packages of D cells in reserve (some are out-dated, or nearly so). During a power outage, I gave away a 3D lantern to a neighbor, who wasn't sure if he had a working flashlight, and an auto-on, plug into an outlet, emergency power failure light, similar to the one posted above.
IMO the auto ON light is a very often, not included essential, in most households.