Shakespeare’s historical plays dramatize the lives of English rulers during the Medieval era. Why are these plays not always historically accurate?

This question raises an important question regarding how we should approach Shakespeare's plays and their role within Elizabethan and Jacobean society.
Shakespeare is largely credited with inventing the history play. These historical dramas had a large audience, as the wars and intrigues of recent rulers playing for power on a grand scale are perfectly suited to live theater.
Shakespeare had a few different sources in addition to general popular understandings of the historical context, but Holinshed's Chronicles seem to be his most common source material. Holinshed was not always accurate, so this might well have skewed Shakespeare's thinking, as would the demands of shaping a sprawling historical event like the War of the Roses into a 5-act play, even as a trilogy.
Yet another and likely more reason for these inaccuracies involve the needs of both commenting on current politics and not upsetting the monarch. For instance, his Richard II was used by Essex to stage a failed coup, nearly landing Shakespeare in trouble. Richard III, on the other hand, seems like a celebration of the Tudor victory over the York monarchy. James likely found favor with Macbeth in that it also praised his family line. In critiquing the nature of power, however, Shakespeare's plays cut to the heart of the nature of human affairs. Rather than a history lesson, then, the plays are more properly a lesson in humanity, using history as a context.