Honestly, no. At least not with it being only acceptable by the one class. Reason being, the game is meant to be played alongside guardians of different classes. While it has a single player aspect to it, the fundamentals would not be there with a mission designed for a single class. However, if it were one that all classes could do, and all get some reward with the class it is meant for getting a bonus item such as a garb or something, or having all 3 classes going through the same thing with parts in the quest playing to a specific class, then it would work. I have plenty of times (or should I said had, during beta) that I was not with my fireteam and running solo, which would be the time to do a mission as you brought to mind, however I would feel that I have to leave my team to do something of the sort which I likely won't want to do anytime soon. With a lore quest for a class I see it as better to do at the beginning to fully understand things prior to everything else being done. They could however have it as something you do before you get to the tower and meet up with friends, but that would mean they would have to change the start which is not an option this close to release. So, while I would love to have something going in to more depth of the classes, I would not want it quite under the design you had thought out. As said in the beginning, I see this game as fundamentally designed fully in its multiplayer aspect. Can never have too much lore though, so the basic idea of your quest would be nice.