Well known fact for years, and I don't know why, nor can I analyse it: a B737 rolls off the wind on rotation. i.e. when rotating you need to increase aileron into the wind. Nothing to do with rudder, just a fact of doing it for years.
On takeoff roll you have some rudder down wind and will have some aileron into wind near Vr. On rotation, because of this 'roll off' tendancy you need to increase into-wind aileron to keep wings level. This increases the cross control configuration. The natural roll-off is aided by the down-wind rudder. This is where I have a hesitation in agreeing with the FCTM, even if that is blasphemy. It says smoothly neutalise controls once airborne. The down wind rudder is counteracting the weather cock factor ON the Ground. Ideally you want the a/c to head INTO the wind on liftoff to maintain Rwy track. The roll-off and rudder are countering this. If you slowly release the rudder at rotation the amount of extra into wind aileron needed is less. This leads to less spoiler delection etc, etc. and results in a less drag confuration at liftoff. It also means you are not cross controlled at actual liftoff.
It's just what I've found works on real a/c.
KISS.