Fair enough, but if God is going to hide whenever people try to look for him in a rational way, then he can't blame them for not believing in him.I don't know if this is an actual study that exists, but I can see logically how, if it does, it could cause one to favor the placebo idea.... I do not think a sign is even close to enough to convince someone of something they don't want to believe, and I don't think God is interested in doing that anyway.
I think you took this to be more negative than it was meant. It's also not a direct quote, just what I remember. I think what Feuerbach meant is that prayer is just an objectification of what people want. This is not because people are praying for selfish reason all the time, because certainly they aren't as you have clearly demonstrated. By praying people express what they want, be it humility or whatever, to themselves. In this way they can influence their state of mind as Dodens was discussing earlier.What about a man who prays for humility? A man who prays for his enemies? A man who is sick praying for healing, but adding in that he pray for God's will above all, regardless of what it is? I think you and Feuerbach are confused as to what Christianity teaches.
I've probably done a very bad job of explaining his views, but if you're interested I'd at least check out his wikipedia page. I find him pretty interesting and he was pretty influential to his contemporaries.