The reason why shutdown is effective against players (both in PvP and PvE) is because they have strategy and synergy. Their power primarily comes from their builds, the way they work together, and the way they use them. Hence, shutdown vastly decreases their effectiveness, because they've specialized themselves for doing something (even the most "general" of usable warrior builds is still specialized; the only warrior builds that are unspecialized enough to be truly "general" are crappy warriors who try to spam flare).
Moreover, shutdown also ruins a player's momentum and puts them into a situation different from the norm which they must now deal with. Now they have to change their playstyle in a way that is not as optimal as they would have liked, or suffer the consequences (whatever they may be).
Against monsters in PvE, none of these factors exist. Monsters have crappy builds full of useless skills, predictable AI, little synergy with one another, and no true teamwork. Their power comes almost entirely from their insane levels. Hence, the only thing shutdown accomplishes in PvE is preventing damage. But there are far better options for that, especially considering the various passive defenses monsters have against certain forms of shutdown (such as energy denial).
It is for this reason that the mesmer is less than optimal for PvE, despite it's prominent place in PvP. There's really no if's, and's, or but's about it. As long as we take as true the assumption that shutdown prevents less damage than other, more direct methods (and I'd have to ask one what they were smoking if they didn't), then mesmers as they are currently designed will not be anywhere near as effective in PvE as the ones that dominate the meta.
Are mesmers useless? No, I'd stop short of saying that. They can spam EVAS better than anyone else, for example (the only other profession combo that can compete there is A/Me, and even then, Mesmers can either take Mindbender in addition to FC or just take FC and leave themselves a free PvE slot to work with).
That does not mean, however, that mesmers don't need a buff. There's really no question that they need one. The question is, how to go about it? What skills/monsters/whatever need to be changed (and in what way) in order to facilitate mesmers becoming more useful in PvE?
There have been a lot of good ideas so far, and it's that direction I think we need to continue in (I'll stay on the sidelines, though; I prefer to make suggestions about professions I actually know something about

).