Add to this the fact that the theatre was, at the end of the day, a mechanism for propaganda as much as it was anything else; all plays had to be approved by the Master of the Revels, and theatrical performances were subject to heavy censorship from the Elizabethan/Jacobian dictatorships. Elizabethan/early modern authors were very conscious of the fact that they were shaping the public's understanding of historical events for political purposes -- this was not something they shied away from. Hence why King MacBeth is the epitome of temptation and corruption, and the ancestors of King James are depicted so heroically.
And then there's Richard III, which is a very good play, but it reads like a propaganda piece more than everything ... Not surprising, considering Richard was the one whom Elizabeth I's granddad defeated on his way to the throne. Not that historical Richard III was a saint or something, but Shakespeare presents him as a complete monster devoid of humanity.
And on the flip side, there's Henry V
, which depicts the title character in such unambiguously heroic terms that it would rival a North Korean biography of Kim Il-Sung in terms of being cult-of-personality propaganda.
But then, part of Shakespeare's genius was his ability to compose works of propaganda that are nonetheless brilliant, compelling stories.