Movies tend to make things look more interesting and exciting than they are in real life and forensic psychology is not an exception.
I think creators of crime dramas include elements of forensic psychology so that the audience can be involved in "figuring out" the subject. People notice patterns, and when someone deviates from expected behavioral patterns (criminal behavior, for example), we experience tension. Show creators know that this tension/suspense is what keeps people watching.
The forensic psychology bit is also intellectually stimulating for audiences. It's fun to follow clues and piece information together. Plus, people can gather insights from what they learn and use it in their everyday life. Then, generally, there is a break in the case, a deeper understanding of the subject, and finally, resolution that leads to catharsis for the audience.
All in all, I think crime dramas showcase an entertaining version of forensic psychology to draw in audiences and allow them to also participate in the show.