Current policy is to have trainer battle and rival battle music from Gen 4 and later as background music. For unspecified reasons, I can't add too much music, but if there's other music you'd want, feel free to be more specific.
New music every month is definitely way too much for us to support. Unless it was on rotation or something. That might be an interesting possibility.
One thing that has been a longtime desire of mine is to hear the actual music of the generation I'm playing. When I'm playing ADV, I want to hear RSE music just like I am seeing RSE graphics, like the trainer battle theme or the champion theme.
As it stands, it's comparable to a scenario where there'd be no RSE sprites at all and instead playing with the 3D models Pokemon has been using since Gen VI. It really takes away from the feel and experience and has led me to simply mute the music altogether.
This could be a suggestion thread topic in itself, but in essence, it would be wonderful if past gens only had the music from their actual generation play during battles---even just two or three select tracks for the rest of time (again, with Trainer Battle, Rival Battle, and Champion Battle themes being simple no-brainers).
Furthermore, it would be really nice to be able to control what music you hear for your battles in the first place, rather than it being completely random and not up to anyone. But as I've read, this is not at all an original suggestion.