usted = tú
if usted = tú = you, then why is "Usted escribe unas cartas" correct? Would you say "Tú escribe?"
A simpler way of explaining this, perhaps, is that "Usted" and "Tú" are like "thou" and "you" in English.
You have to use a different verb ("You have", but "Thou hast"). Spanish, unlike English, still has the formal pronouns. So they're not exactly the same. They both refer to the person you're talking to, but one is formal and the other isn't.
I'm not an expert here, but that's how it makes sense to me.
"Functionally, usted and ustedes are second person pronouns, but grammatically, the verbs they govern are conjugated in the third person"
usted is just a more fancy way to say you. it is like the english "sir". would sir like a cup of tea?