Lots of interesting replies to my OP...
I was taking it a lot more simplistically, I guess, but part of that was the way the sign was worded.
For many Christians, prayer is, on a day-to-day, normal basis, more about reflection. Whether God gives them the answers to their questions and problems, or whether the quiet time spent simply pondering them brings an answer to light is a matter of perspective, and it's pretty much impossible to convince them that their own minds are capable of working something through to a good solution.
Then there are prayers of thanksgiving, which also, plainly, have nothing to do with wishing. Or worshipful prayer, which I suppose could be seen as hedging your bets and keeping on god's good side.
But the way the sign was worded, it just sounded as though plain old wishing for something to turn out a particular way was pointless, whereas praying for the same thing was useful.
I guess, as has been said many times in the past, it gives people the illusion that they have some sort of control over the outcome. Wishing is impotent, but prayer, ah, that's somehow different.
But since the whole ultimate plan is supposedly in god's hands anyway, why can't they see that prayer and wishing give exactly the same result?