They're not really particularly low power.

Quick search suggests around 8W power consumption with a 2 ohm heater, which at the approximately 4V of a charged Lithium-Ion battery (V=IR, P=VI) checks out to around a 2A draw.

Similar results suggest the batteries inside are in the neighbourhood of 0.75Ah (3.7V nominal) = 2.8Wh. I don't know how much of that capacity actually gets used during the "lifespan" of the vape, but I'd guess half would be a good estimate. In any case, probably safe to assume you need to pack around 2Wh in at minimum.

A Lithium AA battery (Li-FeS2 chemistry) gives you 3.4Ah @ 1.5V = 5.1Wh, but has a maximum discharge current of 2.5A (only 3.8W). The AAA is only 1.2Ah with 1.5A discharge, but two of them would give you 3.6Wh and 4.5W, closer to the target but still under.

You could probably arrange this in some sort of configuration whereby the batteries charge a capacitor and that runs the heater, at those kind of numbers it'd need to be at most a 2 seconds off for 1 second on deal, but that honestly seems like it should be fine for, y'know, vaping. Might just need to have an on/off switch to avoid draining the batteries when you're not using it.

But I guess we're at the point where manufacturing Li-Po cells happens in such vast quantities that the extra electronics to charge a capacitor from a 1.5V battery probably cost more.

There are lithium primary cells that are perfect for low power uses when you need something to last years in between battery changes. They can't supply high current, which is why rechargeable batteries are used in disposable vapes even though it's very wasteful.

They should either ban disposable vapes outright or put a large enough deposit on them that most people will return them for recycling.