Possible Solution:

When at the ammo/supply crates, once the backpack is acquired, have the ammo/supply crate save/remember the backpack radio's on/off state, and/or as well as possibly the frequency.

Another possibility, when transmitting, automatically select the radio with the longest range capability. However, there maybe times when players choose to use a radio with less power, or use a radio with the shorter transmitting range. I'm more so for having the ammo/supply crate save the radios' state of power on/off and frequencies.

Another solution, have the backpack radio powered off by default, as most radios picked-up in real life are turned off by default. However, the 'R' key (while hovering over frequency) is not documented within the pop-up help prompts, denoting how to turn-off radios, or last I checked. The process of turning on/off radios is not fluid, or is very finicky.