My goodness you're authoritive for someone who has never flown the aircraft you are giving advice on.
I think you may have mis-read the book or are reading from the landing section where you increase aileron deflection as the speed decreases and the ailerons become less effective.
I find it hard to believe that Boeing would publish something like this.
Different machinary, different techniques required. Boeing did publish that,it is a direct cut and paste from the latest update
The goal should be to hit neutral just before rotation speed, pull the airplane off the runway, and adjust bank angle as appropriate.
That aint gunna be pretty in a 737.