Not wanting to kill the princess is understandable, but in a war situation could've been a fatal mistake.
However, no royal or person in power over a country is "innocent" even the princess. Sure, she may have been a side character through the whole thing, not involved directly in making the decisions, but this is a scenario where bloodline means something IMPORTANT. Just for being born who you are born, you have certain privileges and responsibilities and worth. Your place on earth is predestined based on who your parents are. Your body itself is worth something differently than another person.
A few situations come to mind. People with means and power can rally around the princess in name only and cause an insurrection. Or the princess could bear a child and raise that child to be a merciless tyrant or claim rights to the throne or declare independence. No one knows what may happen in the future, however, the 100% surefire way of making sure that doesn't happen is for her to die today.
It is a timeless and age-old method of the conquerers to root out any means of a future headache. It is objectively a 100% safer way to handle any future potential lives lost from a war.
If this sort of view didn't come to mind, then you are purely reacting to this one situation and not thinking ahead. Fortunately, these commanders and tacticians and emperors are trained to think that far ahead.