Hello guys,
I was briefed during my type rating that the Boeing technique for crosswind take-off has to do with the swept wing.
Not 100% sure about this but I think it was this.
The wing which is on the crosswind side gets air over the wings at an higher angle (closer to perpendicular) than the wing on the other side (closer to parallel). So the wing on the crosswind side is creating more lift and this needs to be countered by applying aileron into the wind. As speed increases the effects gets bigger, so more aileron needed.