Who has the infrastructure to account and pay for this sort of stuff? Professional broadcasters, mostly.
This assumes the music was written by an association composer. Perhaps you have some unsigned band that has granted you permission to use their material. You're clean.
Beyond music, there's spoken word. Performances have value, but many of the podcasts I've heard were more akin to written blogs than produced audio programming.
What Apple could do here, if they're so inclined, is to swing a podcast deal with their labels. Music purchased from the iTunes store would be licensed for personal use as it is now and non-commercial podcasting. If iTunes could be retooled to record voice-overs -- and it sounds if that may be coming -- you could build a podcast within iTunes and distribute it via Apple's music store. The podcasts would be playable through iTunes.
Apple's motivation in this is twofold: it would encourage podcasters to use Apple's platform and purchase their library through the Apple Store, and the podcast songs would be clickable. Listeners could buy whatever they like as they hear it.
It's a proprietary solution, but would finesse the licensing issue and make music podcasting more accessable.