The most profitable model I've ever heard of for music was the jukebox. 25 cents to listen to a song, whether or not you owned it, regardless of how many times you've played it - and all without the guarantee that it would even play before you left the establishment. And I don't remember anyone complaining about the cost.
So what if there was a service which functioned as a jukebox, but with a monthly service fee instead of a per song fee. Now, there's nothing revolutionary about that of course, plenty of attempts have been made at doing just that. The problem with those models is that they didn't have enough content to automatically entice users to discover (and hence pay to listen to) enough new music to make it profitable.
But if you had a large enough library that you could create various types of iTunes-type genius playlists based on things like:
2nd favourite songs of people who listed the same favourite song as you
Songs/albums manually suggested by the actual artist of the song you're listening to
It would take both a tremendous amount of content to generate truly successful recommendations, as well as way of uploading records of your preferences/familiarity from various music programs such as iTunes xml.
In addition to that, there would be ample upselling opportunities - a section displaying available live concerts from the artist playing, a section for merchandise from the artist, maybe even sections for music learning products such as video lessons which included the song being played, or learning materials created by the artist. With enough users, and the ubiquitous face book links, sections could be created where people could join others wishing to carpool a local concert (and or chaperons for minors wishing to attend).
Again, I'm aware that all the capabilities exist in spades across all the various balkanized music services; but none of them have every gotten enough cooperation from music publishers to achieve the critical mass necessary to add sufficient value to make people comfortable paying a monthly fee to possibly do little more than listen to what might be in their own library with greater ease of use.
As for the licensing fees for the music, the monthly fee's net profit could easily be proportioned to actually publishers of the music that was heard.
Full disclosure: a big part of the motivation for wanting to see a service like this succeed, is to finally drive music profits to the artists creating the music people listen to. Right now, the artists making money are the ones that are popular among people who don't know how to get music for free; not the artists that are popular among people who are actually listening to music. This would also have the effect of driving home the value of albums or songs that people keep listening to years after their release, hopefully nudging the music industry into investing more in artists that have more going for them than nice tits and a copy of Antares auto-tune.