I would love it if there were in game "surprise" events that players had a stake in participating in. That is, an event such as a borg invasion of Q'onos, which if not repelled would result in Q'onos' evacuation and players would lose access to Q'onos until the borg were pushed out. Thus, if a player really doesn't feel like engaging the borg invasion, they really don't have to; other players would likely participate and if the borg invasion is not immediately repelled there is no permanent damage to the player-- yet when making the decision and for those who do participate, there is a certain stake in the event. The combination of surprise and the stake would give events a feel that is more "real".
I'm sure there would be some logistical stuff too but overall I think if you balanced the risk it would be ok. Obviously the event can't be impossible to overcome, but if a player doesn't participate they really don't lose out on anything other than the experience: Q'onos would still be liberated and everything you can do at Q'onos you can do somewhere else anyways (other than the stuff at the Academy).
Maybe I'll just try to convince some players first, but either way I'd love it! Even if there were smaller surprises, like a rogue Romulan warbird attacking a Klingon mining world or something random but storyline like that.