But for purposes of answering Joseph's original question, (which was why did the letters came to rival the gospels in authority), it doesn't matter whether they were real letters or constructed, because when they were accepted as authoritative everybody thought they were letters.
Actually, I think the reverse question should also be asked: Why did the gospels--which appeared *after* the letter of Paul, come to be accepted as authoritatively as Paul's letters?
Especially for a gospel like "Mark" which had no obvious connection to any apostolic authority--or even Marcion's gospel, which explicitly did *not* claim any apostolic authority.
A partial answer to my flipped question would be that it took a big P.R. effort, including naming the Gospels in a way which connected them with the apostles, retcon-ing "Mark" as being "John Mark", etc etc. We can, as it were, see it happening in "real time" in the writings of Irenaeus and Tertullian.