We can can rest assured that Ferdinand and Miranda will be good rulers. Across many of his plays, Shakespeare explores the qualities that make good monarchs. These include modesty, "meekness," by which Shakespeare means not being bloodthirsty or vengeful, compassion, and an ability to put the needs of others ahead of one's own. Ferdinand and Miranda have all of these qualities.

Rather than show they are weak, the trials Ferdinand and Miranda undergo prove them worthy for leadership and one other. Though Prospero knows from the start that he wants the couple to wed and rule, he feels they, Ferdinand especially, should not come by their rewards too easily. He knows that what is struggled for is valued. 

Prospero puts Ferdinand to the test by having him drag logs; this is a humble task more likely to be assigned to Caliban than someone like Ferdinand. The fact that Ferdinand does the task wilingly shows his modesty and good heart. Ferdinand is also able to control his lust, a symbol of all the passions, meaning he will be a levelheaded ruler. Miranda has been carefully taught by her father and shows compassion, such as when she wants her father to calm the storm that will shipwreck the passengers on the island. Both she and Ferdinand will be just rulers.

We really do not know what sort of rulers Ferdinand and Miranda will be, as they are both quite young and naive in the play, and we do not see them in positions of leadership.

Ferdinand seems an honorable young man, willing to work hard to win Miranda. He is quite conventional, following the behavioral and ethical norms of his culture scrupulously. There is no evidence that he would be a bad ruler but no real evidence that he would be a great one, as he does not display any great evidence of intelligence, originality, or leadership skills but seems more a responsible follower than a leader. As he grows older, he may become stronger, but he strikes me as average, likely neither to do great good nor great evil and to be guided by his advisers rather than to be particularly original.

The role of female royalty was normally to produce "an heir and a spare" and not to cause a scandal. Miranda is a pleasant young woman likely to behave with a certain propriety. Her upbringing on the island may be a disadvantage, as she would lack a powerful network of friends, not know much about court intrigue, and lack knowledge of the minutiae of court etiquette, because Prospero, a father focused on his own scientific and philosophical pursuits, would probably not know much about female court culture.

It is difficult to determine with certainty whether Ferdinand and Miranda will be weak leaders, but they will likely be kind and just rulers. Prospero partially controls Miranda, a teenage girl and his own daughter, by using magic. He also uses sorcery to manipulate Ferdinand. It is unlikely that Ferdinand and Miranda will have to worry about their fathers controlling them when they come into power. They will have gained in wisdom, their parents may very well be gone, and Prospero will have already given up his wizardry.

Miranda and Ferdinand seem to be tender-hearted youths. She cries when she sees the tempest, begging her father to stop: “I have suffered / With those that I saw suffer.” She not only offers compassion to almost anyone, she speaks up about how she feels, even when her father rebukes her. Ferdinand also shows courage by attempting to fight Prospero, who is able to stop him with magic. Also, Ferdinand is so taken with Miranda, he agrees to Prospero’s tests of menial labor because “she is / Ten times more gentle than her father's crabbed, / And he's composed of harshness.”

From what we know, Ferdinand and Miranda are good people, curious, kindly, and brave. They are manipulated only in extreme circumstances and in their youth, and it is very possible that their resolution and strength will grow with age.