Mattia said: "To make this nice and extreme: Take a section of pipe, any pipe. Take a straightedge. If you run it parallel to the central axis, it'll lie there, on the pipe, niiiice and flat, along the entire length. Now try angling that straighedge a little bit, so it's no longer parallel. So it's like a guitar string on a fixed radius board. What happens: it won't lie flat, without gaps."
True, the gap between the string and the fingerboard (or staightedge and pipe) increases from the nut towards the bridge. But this is exactly what you want to happen anyway, and the radius of the fingerboard is just one factor that determines the height of the bridge saddle for each string. So there is no problem if there is no bending.
"Fact is, all guitar strings, when laid out normally, 'trace out' a conical path (compound radius) and not a cylindrical one (single radius). That's what a compound radius gives you: the arc of the fingerboard changes as you go up the neck."
I think that is a rally good way of understanding how the compound radius helps with bending.