You are correct, now explain why the army radio uses a battery that weighs 3 lbs. and lasts less time than 2 AA batteries in a motorola radio that has longer range?
Do the math. Two AA batteries put out 3V with about 100 mA hrs. No transmitter be sustained for more than a few minutes with those.
Additionally, the military has chosen to use secondary cell (rechargable) as opposed to the cheap commercial primary cell (throw away) batteries.