Does the tempest and colonialism have similarties

When a country or a power tries to colonize something they bring there culture and customs to the region that they think is needed to be colonized. In the imperial age the name of the game was colonization and if you had the most territory you had the most power which everyone strives for. In a sense you can say that Caliban is the Native Americans for instance and Prospero is England trying to educate and civilize Caliban cause in his cultural he is a savage. Also there was a moment in time were Caliban and Prospero were able to coexist with one another, but Caliban broke this trustworthy bond between them by attempting to have his way with his daughter Miranda. As soon as Prospero found out the trust was broken and Caliban was sentenced to a cave were he lives now, and is now Prospero slave. The parallel I'm trying to depict is when , the Native Americans had a trust bond with the pilgrims and when the Natives broke that, the pilgrims didn't take it lightly and they were punished, but is it right to colonize a "savage" culture or does that culture think the colonizers are the savage ones ?