This is a somewhat odd play from Shakespeare, but I think it is precisely its oddness which makes it relevant today. His king is not portrayed as a "great" figure (whether for good or for bad), as one expects from the tragedies and histories. Instead, the plot resembles nothing so much as a family quarrel, played out over the battleground of France. The two queens hatred for one another seems oddly unmotivated; indeed, we learn little about the motivations of the characters throughout the play. King John's death at the end is equally random. It is not the result of an intrigue that has developed throughout the play, or at least not one which we, the audience have been made party to. We simply learn that he has been poisoned, and he comes onstage to die.
Our sympathy instead lies with the ordinary people, those who must suffer from the power struggles and personal feuds of kings, and those from whose perspective, I suspect, the play is presented: the townspeople of Algiers, who close their gates to the kings who are battling over their town like some choice plaything (those who have suffered through a particularly vicious election may sympathize with this decision); Hubert, who must make the choice of obeying the king or acting according to his conscience when asked to kill young Arthur, and whom the king subsequently berates for not preventing him (the king) from giving the order to do so when Arthur's death turns out to have been a bad political decision. And of course the Bastard, who provides an ironic commentary on the events as they happen. Here, too, the royals appear like spoiled children under whose power their subjects must suffer.