Like we've said, Shakespeare wrote Richard III when Queen Elizabeth I was on the throne. As we know, Elizabeth I's grandfather was none other than Henry, Earl of Richmond – a.k.a. Richmond, a.k.a. King Henry VII, a.k.a. the guy who bumped Richard III off the throne and established the Tudor dynasty.
Not long after Richard III was taken down, the Tudors and their supporters (like the historian Sir Thomas More) began a smear campaign against Richard III in order to make the Tudor dynasty seem more legitimate. As literary critic Stephen Greenblatt reminds us, said smear campaign involved portraying Richard as a "monster of evil, a creature whose moral viciousness was vividly stamped on his twisted body."
Historians and literary scholars call this the "Tudor myth." It basically says that the Wars of the Roses and King Richard III's so-called wicked reign were one of the darkest periods in English history. That is, until King Henry VII's divinely sanctioned reign brought about a time of peace and prosperity in England.
Like we said, Henry VII was the grandfather of Shakespeare's very own monarch, Elizabeth I, so Shakespeare is sort of obligated to promote the idea that the Tudors brought about a golden age in England. Not only that, but Henry VII's reign was divinely sanctioned, meaning God supposedly wanted him on the throne.