IMHO, lowered background noise when you switch to battery power indicates that your equipment's power supplies, or the grounding scheme of your system ain't so hot. I have never had a system, cheap or expensive, that I could not get to be quiet. Sometimes it took quite a bit of trial and error experimentation.
One exception would be tube electronics (Heathkit preamp) that used AC filiament excitation, where I couldn't get the hum to completely go away. This was back in the 1950's.
One exception would be tube electronics (Heathkit preamp) that used AC filiament excitation, where I couldn't get the hum to completely go away. This was back in the 1950's.