In such a situation, a person would first be in denial and would doubt the validity of the horrible thing that they just heard. Then, a person has to come to grips with what to do about it (Mills is a cop, and most have a great respect for lawful acts). That covers it for real human experience.
This is a movie, and by stretching it out, it helps engage the viewers, creates suspense, so it is an effective manner to create a good movie viewing experience. So that is why it was written and acted out in that manner.