Apparently it’s less like a letter, and more of a sermon format, or even multiple sermons on the same topic. (Three seems like a common scholarly guess.) And if they are sermons, it’s not the kind done in church, but more of an educational and encouraging preaching outside of church.
So in that case, it would make sense for St. Paul to have a more formal way of expressing himself than he would use in letters. Speeches and exhortations were supposed to be formal, and to make clever references, like the reference to the Odyssey. All the Scripture quotations would fit right in.
But if other communities were asking to be sent transcripts of this cool sermon series, a transcript could easily be turned into a letter by adding a postscript.
Anyway, it’s interesting to be thinking about salvation history during Advent.