Although the plays are written about individual kings, I think that Shakespeare used the plays as an opportunity to voice his opinion on kings and kingship in general. This was assisted by the fact that he was not prohibited by the true events, because it is well known that all of Shakespeare's plays were written purely for entertainment value, not as a historical record of what occurred.
The main notion of kingship that Shakespeare attacks in Macbeth, King Richard II and King Henry IV, is the divine right of kings, where the kings claimed that they were God's counterpart on Earth, and a 'step up' in divinity from the other aristocrats and the common people. In his plays, Shakespeare depicts the kings, and Hal, in King Henry IV, as people who were not, or at least did not act like the direct descendants of God. In Macbeth, he commits treason and murder, the two worst crimes of the day, and neither Duncan nor Macbeth were saved by God, who, according to the theory of the divine right of kings, should have saved Duncan and then Macbeth. When they were killed, they were both king, and therefore the right-hand man of God, the creator, who controls the entire world and who could have stopped them from being killed.
In Richard II, Richard bankrupts the country with his blatant mismanagement and his excessive spending on his 'favourites', who are already rich aristocrats, while ignoring the common people who are living in poverty. Richard's behaviour leads to both the aristocracy and the common people disliking him. The aristocrats disliked him because he was bankrupting the country, which they did