Jacob’s oath facilitated an avenue for Joseph to apply pressure to Pharaoh without jeopardizing his own position by saying that it is his father’s wish to be buried in Egypt, not Joseph’s. He wanted to reassure Pharaoh that his trust in him was well placed. He was able to convince Pharaoh that he indeed considered Egypt as his home. However in this case he was now powerless to change his father’s burial place, having taken an oath to bury him in Canaan. Pharaoh had no choice but to relent, though perhaps the incident left a lasting impression on Pharaoh and his subsequent treatment of the Jews as foreigners and a potential threat to his kingdom, as described in the beginning of the Book of Exodus.
We now understand why Joseph was so sensitive and careful in how he phrased the request to bury his father in Canaan to Pharaoh. He sent messengers to Pharaoh to ask in a roundabout way, saying that he himself is acting as an agent of his father who requested to be buried in Canaan. Joseph wanted to stress that he was not rejecting his status as an Egyptian. He acted in order to preserve his status of Egyptian Royalty and ensure the survival of the children of Israel as they embarked on a path to become a great nation born in Egyptian exile.