Not many playwrites besides Shakespeare wrote histories, so the fact that our selection is comprised entirely of works by the Bard reflects his monopoly rather than our selective abilities. Histories should not be confused with "problem plays," though they often are by those who think "tragedy" and "comedy" are the only viable dramatic forms.
A problem play refers to those works by Shakespeare that fall into none of the three established genres of tragedy, comedy and history. A history, on the other hand, is simply a play that revolves around historical figures. This doesn't mean a history play is the result of research, or that any of its content is accurate or reflects real events. It simply means that the main character is someone like King Richard III of England, or Julius Caesar, or Antony and Cleopatra. Whether the characters in the play resemble the real people on which they're based is immaterial.
If you think this demonstrates a careless disregard for truth, or a groundless postmodern relativism, consider this—if Shakespeare wanted to communicate the actual nature of historical figures and events, why did he choose fictional plays as his medium instead of history books? History as a formal independent study already existed in his day, so it's not viable to suggest drama was the only genre available to him.
Good playwrites aren't concerned with "what really happened" but with "what really is." Their subject is human beings. How humans behave and what motivates them doesn't substantially change from age to age, and so Shakespeare could write about fictional Italian princes, witches and brigands, or Henry VIII as he chose with equal perception and accuracy. He wasn't writing about Agincourt in Henry V, he was showing how men behave under duress, both brave men and cowards, the faithful and the traitors.
Don't read Macbeth hoping for an accurate portrait of the Scottish warlord; read it to better understand how and why men covet power, and what they'll do to gain it. Julius Caesar is about friendship and ideals in conflict, not the greatest general of the Roman Empire. Whether Richard III was really an evil killer of children doesn't really matter; for Shakespeare's purposes, he was.
Misunderstanding the relative roles of literature and historical enquiry has led many to reject fiction altogether. But a good play isn't merely presentational, it's a commentary on human nature. Good history is, too, but its chief material is actual events, whereas a play's chief material is the human heart. These histories are some of the most perceptive investigations of humanity ever undertaken, and reflect the observations and thoughts of a shadowy man many claim was the greatest writer the world has ever known.