The belt packs typically do a lot more than to amplify ambient noise, they also handle RF, depending on the model decryption of the audio signal, EQ as well as other stuff. All while typically running on 2x1,5V AA batteries.

Audio gear isn't made to last long on batteries, it's made to be reliable for the hours a show typically lasts. I worked part-time as a sound tech (paid hobby) for 15+ years, and I never started a show without fresh batteries, regardless of what the indicators on the transmitters/receivers told me.