I’m not an expert on electronics, but I would assume this requires hardware to charge the batteries properly (and I’m not even sure NiMh, which is most AA/AAA batteries are well suited for use in a smartphone*), or using cells with built-in circuits like a 10440. Total capacity wouldn’t be higher than the current battery. At the same time it would add bulk and weight that most users would find annoying. That being said, it’s conceivable that an enthusiast may be able to design and 3D print a custom back cover that could accommodate required adaptor and circuitry.
Somewhat relevant: There’s some discussion about battery frames (though not for standard batteries) in this topic here.
* Charging in phone may produce too much heat; not sure whether it can reliably discharge fast or long enough enough to keep up with demand (discharge curves); suffers too much from a memory effect (leading to more battery waste).