Tomas recently posted an article asking "Does Healing Suck?". There are many reasons why many people don't like healing, including social and mechanical reasons. Here are some reasons. I doubt any of these complaints will be fixed by WoW. But perhaps a future game will consider the problems faced by healers. As this will probably get quite long, I'll go one issue at a time.
Issue #1: A healer interacts with the interface, not the game.
WoW has this really pretty game, with interestingly designed monsters. Too bad a healer doesn't see any of it. All a healer sees are the raid's health bars. When I was healbotting, I honestly could not tell you what the bosses looked like.
Now, a healer still has to pay attention to the battlefield, but they have to split that attention with the health bars. And really, all you watch for are the little cues that tell you you have to run somewhere to avoid some random effect.
If you pressed Ctrl-Z and the interface dropped away, could you still play the game? If you were a tank or dps, you could. You wouldn't be as effective, and you'd probably hear a lot of "Need more rage", but you could still play. Could a healer do the same thing? No, of course not!
It's telling that one of the major reasons that I use the sRaidframes UI is that the UI will show me when someone is out of range. By making me interact with the game less, I become a better healer.