Upon reading it a few times, the syntax sounds alright to me, but I see why you are asking about this. Typically, the past perfect is used to describe an event that occurred before another event, both of which occurred in the past. For example, "By the time I arrived at school, my teacher had already left." I think the case you are presenting here is a little different, though.
When I think about storytelling, and whether it would sound better to say "it had reached him" or "it reached him" in the context of making a story sound interesting, my feeling is that saying "it had reached him the next day" is better at expressing the progress of time and the continuous flow of events in a story. Being a perfect tense, it gives the sense of covering a span of time (from the date on the letter to the next day when he received it) instead of merely one timepoint in isolation. In this way, the story feels more flowing and more engaging, instead of being a description of several discrete points in time that are not connected.
The difference between "it had reached him" and "it reached him" is comparable to the use of the present perfect tense versus the present tense. Let's pretend that I mailed someone a package, and it is very important to me that it be delivered to them without any problems. If I receive a delivery confirmation that says the recipient successfully received the package, I could say "The package arrived at its destination" or "The package has arrived at its destination." To me, the second one sounds more dramatic and indicates that there has been a lot leading up to this moment, but now that action has finally come to completion. The first one is more bland, simply stating that the arrival occurred, but not suggesting much about anything leading up to that point. I think the same is true for the example you are asking about.