Is Caliban's tragedy necessary for Prospero's romance in The Tempest?

Prospero does not have a romance in The Tempest by William Shakespeare. Prospero is a widower, whose wife (Miranda's mother) died sometime before the action of the play begins. The only woman who appears in the play is Miranda, Prospero's daughter. The only romance in the play is between Ferdinand and Miranda. 

Caliban is not precisely a tragic hero. He exists somewhere between the rude rustics of comedy and the villains of tragedy . He is the son of a sorcerer Sycorax, who ruled the island before the arrival of Prospero. He is a deformed and monstrous character, whom some critics consider a representation of the fears of European colonial powers of the natives of the lands they colonized. As Caliban did once try to rape Miranda, Prospero does need to subjugate Caliban for the safety of his daughter, but Caliban's narrative arc is not a tragedy, and Caliban does...