Cade declares that his new kingdom will only honor workmen, so artisans or skilled laborers will fall in rank. His rhetoric echoes a tradition of popular radicalism, which stressed that there was as much nobility in the labor of an honest man as in the educated speeches of a gentleman. With references to this egalitarian tradition, Cade mobilizes the anger of the commoners against the nobles, directing most of his violence against those can who read or write.
Yet Cade contradicts these same egalitarian claims by insisting that he will someday be king, and from his mouth will come the new law of the land. His army seems to recognize his hypocrisy, but they don't mind it, as they are stirred on by their dislike of the nobles. And for their part, the nobles too show contempt for other classes. Suffolk is irritated that his captors don't release him when he reveals his identity, and he insists that no one so low could kill him -- of course they do.
Hence Henry's weakness creates risk for the kingdom, but not only from its most disenfranchised members among the common people. Though Cade is shown to be a despicable and vicious character, his death doesn't end the threat of civil war; the real danger to England lies in the ambition of the nobles of the court.
And there are schemes and plots to go around. Buckingham, Somerset and Suffolk plot against Gloucester; Somerset and York vie for power; York allies with Salisbury and Warwick against the other lords; Suffolk and Margaret want to bring all the other nobles down, so that they will be able to reign through the puppet figure of Henry. By the end of the play, enough people have been killed that the sole conflict has dwindled to the struggle between York and Henry. York, with a white rose as his emblem, stakes claim on the throne as the heir of the third son of Edward III. Meanwhile Henry, a Lancaster with a red rose as the emblem of his house, has been the hereditary heir to the throne, but he is the heir of the fourth son of Edward III. York believes a crime was committed when the Lancasters came to the throne and killed king Richard II, a crime which many of Shakespeare's contemporaries blamed for the bloody years of the fifteenth century.