David Marcus was introduced as Admiral Kirk’s son in Star Trek II: The Wrath of Khan. Though Kirk knew he had a son, he’d never met him. At first David didn’t get along with his father, mostly because Kirk was never a part of his life. David finally came to respect Kirk at the end of The Wrath of Khan, even telling him he was proud to be his son.
But David’s life was cut short in Star Trek III: The Search for Spock. In a moment of heroics, David tries to protect Lt. Saavik from a Klingon on the Genesis planet, and he ends up getting stabbed and killed. His death created a deep wellspring of hatred inside Kirk for the Klingons and almost led to his own destruction.
Introducing Kirk’s son only to kill him was cruel. He was simply used as a plot device to explain Kirk’s bitterness toward the Klingons in the final movie. Imagine having Captain Kirk’s son serving in Starfleet. Trying to live up to his father’s legacy would be both challenging and rewarding. And we could have seen a long-term connection between the two, giving Kirk something he’d never really had…family.