One could write a long essay on what is the ideal EDC, and many have in fact been written. Maybe I'll repeat a few thoughts for this erudite thread (thanks, Barrington, for initiating it in such a thoughtful manner).
EDC has a historical pedigree, it comes from a predecessor of the HDS. Basically an easily pocketable yet flexible flashlight covering a variety of needs. Typically has been a 1x123A. The original was a pioneer in using LEDs, maybe could put out 60 lumens on high, then considered amazing. I think it had a clip as well and a distinct metal bezel. The ARC 6 was in that category as well. Note that EDC did NOT mean key-chain sized. Simply a small size that is easily carried, certainly true of the 1x123A form factor.
Why 1x123A? You get the advantages of this light yet powerful and high capacity battery--4.5 Watt-Hours. Very high energy density, higher in fact even than rechargeable Li-Ions per gram. And as LEDs developed, it has remained able to get high outputs at least competitive with bigger Li-Ions when size is an issue. (It cannot compete as you get multi-Li-Ions supporting the huge lumen outputs and high current draws). The 123A was invented by Surefire to support high outputs in its (then) incan flashlights, usually for very short periods of time before running out of juice. But it adapted perfectly to the LED world.
The descendants of this design are still there, the McGizmo Haiku, the HDS itself (after renamings and company changes), the ARC unfortunately no longer, the Oveready Boss perhaps. So these are top EDC choices even today.
What these have is the original advantages but also programming ability, when you get to choose the output levels you want quickly and easily accessible. For example, tap once you get mid level, tap twice get high level, tap three times get low level, etc. Even special modes are available (strobe, SOS, etc.). Also typically excellent quality, and some amazing robustness and resistance to drops, water, etc.
Many who use EDC flashlights have extreme and often unusual demands, such as access to "moonlight" level light outputs. These can only be satisfied with programmability. Also, these particular models are descendants of the original, by makers who were there and have kept the line alive. So they deserve consideration and respect, despite their often high prices.
Now, what do you get vs. more commercial offerings? Basically longevity, style, and faithfulness to the original concept. Don't get me wrong, you can find excellent commercial offerings, personally I used Fenix in the past. But basically what you find over time is that the commercial offerings come and go, but if you have one of the top EDC flashlights you tend to keep it and use it forever (especially if you are willing to have them modestly updated, say to replace the LED with a modern offering).
All of this sounds good, perhaps, but there are other points of view. I'll outline two of them, which are basically there in other posts I've made on this topic in the past.
One is that EDC is a kind of weak concept. In a world where we can have, and have, multiple excellent flashlights, why stick to the EDC concept? I've made fun of it actually as the misplaced desire to have the "one flashlight to rule them all." In reality, as you go about your business, you will find you want a nice big flooder, or a thin and efficient thrower, or UV, or red, or more power with a low level accessible just in case...even without going to caving, diving, and all sorts of other niche needs.
As you have seen, many are willing to carry bigger flashlights with them than the "standard" 1x123A EDC. So logically, many will carry more than one, at which point you want to specialize.
The second thought is actually in line with what you are coming to, which is that the 1xAAA flashlights have by now improved so much that they can do what the old EDC's used to be able to do, at an even quite remarkably smaller size and weight, indeed one where you can attach them to a key-chain with your keys.
And I sort of agree with this, especially now that you have access to the Lithium primary AAA, which has almost half the energy capacity of the 123A and similar per gram energy density.
As to which 1xAAA's, I have used different ones over time, I recall the Liteflux with some fondness, and the stainless-steel Fenix L01 (I think, it's been a while) and E15, but my current best is the Peak Eiger with the QTC. Now the QTC--quantum tunneling composite--approach is not universally liked, and I admit I didn't like it much in v1, but in v2.1 it's improved quite a lot.
Short answer: yes, 1xAAA is a worthy successor to the venerable EDC concept, if you wish to remain within the EDC concept confines, which personally I do not, except in certain circumstances (such as travel when I want to travel light). Even then I may just want access to at least two flashlights and flashlight types, the generalist EDC, plus one with high throw at a relatively small form-factor. If the trip involves access to the beach and swimming, then at least three flashlights to include a diver.
