If it requires too much healing to complete, pure melee or casters are impeded.
If it requires significant amounts of dps, you either have to spec and gear properly for one, single dungeon or pure dps classes simply have a leg up.
If you can't tank or mitigate damage effectively...well, you're dead at the first pull.
Therefore, if you reduce group size and composition to a single participant, the more generic and easy you have to make the dungeon.
And of balancing nine class specific dungeons? Tseric quips, "Do you realize how much time that would take?" And you have to admit -- he's got a point. Would you rather see Blizzard spending their development time working on nine different variations of the same dungeon, or working on nine new dungeons everyone can see?
Of course, as painful as my last PuG was, I might prefer the solo content anyway.