"Due to P-factor, the right-hand engine typically develops its resultant thrust vector at a greater lateral distance from the aircraft's C.G. than the left-hand engine."
P-factor: also known as asymmetric blade effect and asymmetric disc effect, is an
aerodynamic phenomenon
experienced by a moving propeller with a high angle of attack that produces an asymmetrical ceter of thrust
According to the above statement P-factor is experienced only by a moving prop with
HIGH ANGLE OF ATTACK but the propeller does not have a high angle of attack during a take off run.
I understand what you have explained in your post. But what you are saying hold good when the aircraft/propeller are at high angles of attack which then cuases the down going prop to produce more thrust than the up going one. But all this doesn't occur on the ground.