I think your tone may be a little to informal for an undergraduate essay.
It’s as if the word well-educated is having an identity crisis! What does it mean, really? It’s a matter of street-smart vs. book smart. The typical Victorian lady may be well-mannered and all, but she really doesn’t have the necessary knowledge to survive a real crisis. As for the book smart guy, when it comes to asking a girl out on a date, he’s clueless! Now I may be exaggerating a bit but what I’m trying to say is that well-educated person needs to be well-rounded, a mixture of both street smart AND book smart. This person is sociable, can think outside of a textbook yet can also benefit from textbook knowledge. Eureka! That there, madames and monssieurs, is what I call a well-educated individual.
I don't think the terms "street smart" or "book smart" fit within a formal application essay. Using the term "street smart" makes it seem like you feel that social traits are attributed to smartness or intelligence. I don't think that is the case. I personally wouldn't use the phrases "Eureka" and "that there, madames and monssieurs" because of there informality.
The tone that you have established in the essay makes it feel like you are giving some sort of boisterous presentation to a group of friends. Is that what you want the admissions officer to be feeling?
I like the ideas of the essay - just make sure you analyze how you sound to the reader.
Good luck with your essay and admissions process!