I beg to differ.
Your analysis is correct, if the motor is held motionless. Your analysis is wrong, if the motor is allowed to move.
Your analysis is correct, but you didn't state it, in that running a motor at 10v vs. 20v at 50% pwm does create different motor behaviors. You will find that at 20v % 50% pwm, the motor actually rotates faster than it does at a steady 10v.