An EDC light is one you carry even when you don't think you'll need a light. Certainly if I were going anywhere near any caves, I'd bring more lights than just my EDC. Of course everyone's habits are different but I think most of us are unlikely to ever get trapped in a cave with just our EDC lights.
That said, the regular (non Ultra) CMG Infinity is supposed to run for 30+ hours on one AA. It's dimmer than the Arc AA, of course.
The Tek-Tite Trek Lithium is another good "trapped in cave" light; it uses a special 3.6 volt AA sized computer battery, but runs for 100+ hours at useable brightness. It's also extremely tough and waterproof and has no electronics to fail, except for the LED itself. But IMO it's overpriced at around $30.
My favorite EDC these days is the Princeton Tec Blast. It's incandescent with 2aaa's and maybe 1.5 hours runtime, is pretty bright, very lightweight, has a built in pocket clip that doubles as a hat clip, and is cheap enough that it's not upsetting to replace if lost.