I personally like the idea. That being said, I suspect the biggest concern would be how quite often people want to just log on and get started with whatever they wanted to do right away. In 1.0, it wasn't really a consideration, since the login events were only CSs and skip-able [if you hate surprises and story telling].

Going with it though, you wouldn't have to make it "random" per-se. One solution to the duty finder problem would be to only initialize the event if 7 other people of the appropriate job log in at the same time. That would inject a random factor, make it rare, and remove the necessity for a duty finder wait time. You could also make it so that someone can "wake up" before the instance starts, breaking the event for everyone and giving something like a message "You feel like you had a nightmare, but cannot remember it."