LOL that would be one BIG cell phone!
Well, not that big really. Certainly small enough to fit in my average size hand comfortably, in my pockets, and to use. But yes, bigger than some.
They could use AAAs I suppose, but I'd prefer the higher capacity of AAs so I wouldn't have to switch them out as often and charge them.
Just for fun I checked, and I can touch my middle finger and thumb together around 10 AAs. Granted, that would be an uncomfortably big cell phone, but 3 AAs wouldn't be a problem for me at all.
For me the benefits (higher than average capacity & energy, not having to wait for the phone to charge, longer cell life expectancy, easily replaceable cells) would far outweigh the drawbacks of having a marginally wider than average cell phone.