I think you may be getting confused. No AAA has 2.9Ah of capacity - that's a stretch even for AAs. And if you mean using three cells, 3AAA lights put them in series, not in parallel - you get three times the voltage, but the capacity is still the piddling 800mAh, if that, of a single AAA.
We don't like 3AAA lights with powerful LEDs because they draw too much current for that battery setup. 3AAA carrier lights are essentially a cheap way to make a flashlight that'll surprise Joe Average with its output for just long enough to convince him to buy it, without the manufacturer having to bother with things like switchmode driver circuits. At the draw of a high-flux LED the AAAs will sag way below their initial voltage very soon indeed; the flashlight will still make visible light for a long time, but it'll be much dimmer than in the beginning.
This behaviour is very similar to that of keychain lights powered by two CR2016s; however, while there's a good reason why those work like that, in this case it's just to sell cheaply built stuff to people who don't know any better.
A proper flashlight with (more or less) the size of a 3AAA would have a voltage booster (or a full regulator) and run from a single C cell. That would be a much better product.