Because it's a great question (and observation), and because I'm sure others have similar questions, I'm posting my response here:
It’s a very good question, and one which requires a better answer than I can give via e-mail. Consider this a start to a larger conversation.
The first thing to realize is that not everyone thinks like I do. There are those who believe in “intercessionary prayer” – prayers which ask God for a particular result, whether that be health, happiness or victory in baseball. And, there are those of us who don’t. Part of why I keep that prayer in place is to acknowledge those who feel that the prayer is more directly effective than I do. This, of course, brings up the important but complex issue of religious leadership – how much do I impose my own views on the congregation? Knowing where to draw the line is very difficult – I err on the side of openness here, largely because of what an emotional issue health and healing is for many.
But, there’s more to it than that. There’s also an awareness that scientific studies show that people who know they are being prayed for show marked improvement in their healing. In other words, even if these prayers don’t work in a direct, almost magical way, they still might have a profound impact.
Last, and certainly not least, there is the issue of religious metaphor. My kind of faith provides very few opportunities for simple, literal statements. Most religion is, in my view, a kind of sacred poetry, in which we say things which aren’t literally true, but help point us to a larger, ineffable truth. And so, while I certainly don’t believe that God is more likely to heal someone faster simply because we ask God to do so, I do believe that the prayer has other, more subtle meanings, which are true in a different sense. It’s interesting that you picked up on this one prayer, though, because I do believe that, from this point-of-view, it’s one of the most problematic. It’s harder to understand this prayer symbolically than most other prayers; despite all of my explanations, I’m still not 100% comfortable with its inclusion!