Sorry, but could you please tell us which manual is this from? Because it surely isn't Boeing's FCTM for 737, which says (my formatting):
When a smooth continuous rotation is initiated at VR, tail clearance margin is assured because computed takeoff speeds depicted in the PI Chapter of the FCOM, airport analysis, or FMC, are developed to provide adequate tail clearance.
Above 80 knots, relax the forward control column pressure to the neutral position. For optimum takeoff and initial climb performance, initiate a smooth continuous rotation at VR toward 15° of pitch attitude. However, takeoffs at low thrust setting (low excess energy) will result in a lower initial pitch attitude target to achieve the desired climb speed.
The use of stabilizer trim during rotation is not recommended. After liftoff, use the attitude indicator, or indications on the PFD or HUD (HUD equipped airplanes), as the primary pitch reference. The flight director, in conjunction with indicated airspeed and other flight instruments is used to maintain the proper vertical flight path.
Note: The flight director pitch command is not used for rotation.
Who's tracking 2.5 vs 3 degrees per second? No one.
Surely PM and they should speak up if they think rotation rate is excessive.