calipsoli covered the gamut of options available in this space pretty well.
AAA cells are not particularly high power - they are not well suited to very high current draws and your runtime will suffer pretty severely. Not only that, you have such small thermal mass that either you allow the LED to cook itself through little heatsinking, or make one seriously warm and impractical torch if you want a pocket rocket of sorts. There are practical limitations to these things and there is a lot going against AAA cells unless you moderate it appropriately.
I myself offered a AAA light here once in the form of the Zephyr back around 2008, but it wasn't a "huge seller", unfortunately, and the project was shelved (which was a shame, honestly, it was probably my favorite light that I had designed).
Just my $0.02.