The New Testament has Gospels, history (Acts), epistles, and Revelation. It is easy to answer why the New Testament other than the Gospels has this focus: because Jesus in the Gospels often spoke of Heaven, Hell and resurrection. Paul, John, Peter, James, Jude and the author of Hebrews took their lead from their savior, expanding on the topics he covered, as well as additional commentary on the Old Testament.
I once read through all the parables of Jesus and counted how often Jesus spoke of Heaven and how often he spoke of Hell. Slightly over half the parables addressed Hell and eternal judgment, slightly over half addressed Heaven and eternal reward, and many parables mentioned both.
The principal revelation Jesus was working towards, first in riddles and then plainly (in the speeches at the Last Supper in John 13-17), was his coming crucifixion and resurrection. He framed this as a shattering, divisive, determinative event in history. The world was about to be divided in two, and all people needed to make a decision about which side they would be on. This decision would then be ratified by the angels, who wold implement it in some fashion.
The rest of the New Testament showed the beginning of this outworking, as a realignment, as some Jews joined the Church and others did not, as some Greeks joined the church, and others did not, as some Romand joined, and others did not. This ends with Revelation, which describes the final separation of people into two camps.