I’ve never looked at it at that angle.
What I saw was that the story reveals a truth of Christ. When we are baptized and in the state of grace, we’ve ‘put on Christ’. God the Father, decides to see Jesus rather than us sinners, and gives us the blessing. Our Blessed Mother is the interceding Mother to assist us in gaining the blessing.
It could also be a type illustrating how the Jews were the ‘first born son’ that did not care to have the blessing, and the second born son, the Christians, wished so much for the blessing that they ‘stole’ the blessing. Think of when Christ comes to judge the living and the dead at the end of time. When Christ is revealed to the nations, the Jews will wonder how they missed out on the blessing that was intended for them from the beginning. (Sorry, I can’t seem to find quite the right words to illustrate what I mean. Hope you can piece it together.)