Surely half stick gives half elevator deflection?
Not on an A320 (or other Airbuse FBW aircraft) stick position has no bearing on surface position. When the stick is moved the computers position the surface where it should be for the current conditions.
The reasoning behind I was told is to increase load on NLG for better control.
Or maybe it is to over come the effects of the horiziontal stabilizer which is trimmed for takeoff, preventing premature rotation.