There is a lot of devices, that act as a 3G/4G modems and access points. Their weak part is that they use internal battery, which is expensive/not easily replaceable.
The ideal solution would be to have a device, that takes power from 2 or more AA batteries, that are trivial to recharge in bulk or buy at the nearest shop. The combined power of 2 AA batteries is in order of 4000 mAh, which is more than typical power of batteries included in available modems.
I tried of an hour to find any such device, and I failed. Is some reason, why such device doesn't exist, or I simply missed one?