Why Don't We Have Any Letters to Paul?

Several ancient collections of letters published in antiquity contain both letters to and letters from a particular individual. For instance, Cicero's collections of letters contain not only letters written by him but also letters written to him. Same for Pliny the Younger, Jerome, Augustine. But not for Paul.

We don't know where the Pauline letter collection came from. That is, we don't know who collected these letters and why, and how they first started circulating as a collection in antiquity. There have been several theories. Stanley Porter has helpfully summarized the major proposals and advanced his own proposal, most recently in his opening contribution to this edited volume.

The idea that make most sense to me is the one advocated by Porter and several other scholars (e.g., E.R. Richards in this article and this book), that Paul or his secretary saved copies of the letters he wrote (surely this is true) and issued an anthology himself, or left this task to one of his followers. This makes a great deal of sense and accords perfectly with ancient practice (again, Cicero, Pliny, etc.).

But, again, if this hypothesis is correct, why did he not include in his collection any of the letters sent to him? Such an omission would have to be intentional. What reasons could be supposed? The only thing that makes sense to me is that they were not considered authoritative, and the Pauline collection was supposed to contain only 'authoritative' statements from the apostle. Still, in light of the 'occasional' nature of the collection, it would make sense to me to include in the collection some of the letters written to Paul.

I haven't read everything on the topic, so maybe someone has addressed this issue. I see that Porter wonders, if the collection was made from Paul's personal copies, why we don't have the entire Corinthian correspondence or the Letter to the Laodiceans (mentioned at Col. 4:16). 

It is not certain why these letters are missing, unless they simply were not copied originally (Richards [pp. 220-21] suggests that Paul's "severe letter" was sent off in anger and haste) or were themselves lost in the course of Paul's travels, including his shipwrecks. (here, p. 197)

 I don't see anything particularly on my question. Doesn't mean it's not out there.