Having painfully worked to level a WoW character to 70, and having run a small guild that was never big enough to consistently organize even 10 man content, I can understand the frustrations that would be resolved through multiboxing.
On the other hand, it does seem strange to play an MMO by yourself. While I suppose some people enjoy the questing and grinding, and I myself enjoy seeing the new content and acquiring the greatest gear, the basic gameplay itself seems like it is meant only as an enabler for personal interaction. By itself, the content quickly becomes repetitive and boring, but doing it with others offers unique challenges and a chance to play with others.
Mike Rozak, who maintains a blog based around video game design, provided an analysis of World of Warcraft [http://www.mxac.com.au/drt/ProblemSolving.htm] which concluded that the gameplay itself is trivial as long as you have enough people. The actual challenge isn't in killing mobs and accomplishing quests, but in trying to organize the people necessary to do so. If this is truly the case, isn't multiboxing essentially avoiding the problem? Perhaps it could be argued that multiboxing is just another way of solving the problem (changing it into organizing several clients rather than organizing several people), but it does seem to fundamentally change how the game is played.
If not for the fact that you have to buy multiple games and multiple accounts, I would likely do the same for myself. I suspect this is why Blizzard is okay with it -- in the end, they are still getting just as much money, just from the same person instead of multiple people. In fact, it provides the opportunity to get even more money, because it provides the opportunity to sell more subscriptions than there are people who play WoW, and that's already a huge number.