Actually i can think of 2 benefits of being persistently online even if you're just playing single player..

1. Preserving the value of the achievement meta-game. Even if you just play single player, the fact that some players place a great deal of importance of achievements means that it will be a lot harder for players to hack achievements.

2. Blizzard will be able to monitor for cheaters, and with the addition of anti-cheat measures, that orange legendary sword of pwnage will actually be worth something at the auction house, which is probably something you won't be able to avoid even if you're just playing by yourself.

Well, anything is better than the "lagspike and logging back on to find that you have to do a corpse run as a ghost" phenomenon.