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... for me (because fun is personal, right?).
Story instances can make "quests" much more interesting with scripted staged events, and change of environment (because you are in your little world) and there won't be a bunch of other players breaking your immersion.
I have been playing some STO the last few days, and some of the episodes are a lot of fun with multiple location, and different stuff to fight while moving a mini-story ahead. I wish WOW (not that i play it anymore) has more story/event focus dungeons, instead of boss focus dungeons.
DDO also have pretty good story instances (some even have puzzles).
Some of these settings are MUCH more suited (Star Trek in particular) for episode type story missions. Of course aside from interesting missions, combat needs to be good .. and that is probably easier to control in an instance.
Now some may ask .. why do you need a MMO for story instances? I think the answer is .. you don't .. but MMOs fit the bill well. Think about it .. there is no recent Star Trek RPG in the last few years, and STO is the place to be if you want to play story missions, particularly in MP, in the trek universe. Ditto for Dungeons & Dragons.