Under optimal conditions, after an initial set-up of your phone/media library, iTunes would be significantly reduced and there are several things that could happen that could make the software even less relavent.
Optimal conditions are that you have only apps and music and all of that music was purchased from the iTunes Store. After the initial sync with iTunes, matching your tracks with iTunes In The Cloud and setting up all of your address book, calendar, mail syncing, iTunes would hardly need to be used. You can buy all of your music on the phone (which would be available should you choose to open iTunes). If you needed to restore the phone/got a new phone, the initial set-up would be done on the phone, all of your app data would be pulled in from the cloud backup and all of your music would be available to be downloaded on the phone.
If you don't fit into that category (as I suspect many won't), using the iTunes Match service would also help. Adding new music (via CDs, purchases from other stores, torrents) would still have to be done through iTunes but would afterwards be available via iTunes Match.
Another issue would be video, however if iTunes In The Cloud/iTunes Match also gets moved to TV shows/movies then it becomes less of an issue.
Even within the house, if/when the iTunes In The Cloud allows for a streaming option, all of your video/music would be available via the AppleTV without having to keep a computer on/iTunes running. Of course this creates bandwidth concerns, but if getting rid of (and/or minimizing the use of) iTunes is your ultimate goal, it would at least be possible.... maybe not ideal, but the more accessible our data becomes without being tethered to a main computer/software within our house, the less and less relavent I could see iTunes becoming for some people.
