but rather to keep the nose parallel to the runway during rotation.
Not quite...
Rudder (and nosewheel steering, when available prior to nosewheel liftoff) is used to maintain track down the runway centerline. Depending on the airplane and the crosswind component, the airplane may not be aligned with the runway while tracking the centerline.
After the airplane is airborne, rudder pressure is unneeded on most airliners, because the roll spoilers and yaw dampers provide yaw control in turns. So, once the wings are leveled after liftoff, rudder input should no longer be needed. Use aileron input to adjust heading/track outbound.