There are a lot of possible answers to this question, but one is probably that the manner of Caesar's death was highly dramatic; also the whole issue of the murder conspiracy was very topical - there had been plots to murder Queen Elizabeth I, for instance. So for this and other reasons, Shakespeare and his audience would have been interested in the way Caesar died and the motives of his killers. Also, most of his history plays have a strong focus on the main character's death, so it's not unusual. Hope this helps.
