This answer is from the perspective of the hemeneutic previously referred to as 'sensus plenior'; so-called because it purports to be able to exegete the Old Testament the way the NT authors did; expounding God's intended meaning of which, the human authors were unaware.
The foundation - it's all about teaching
In the study of 'the mystery, hidden from the beginning', The Hermeneutic of Notarikon reveals that Elohim means "God אל separated from creation י ; finished by the Son ם , by ignorance ה ". Israel means 'man יש joined to God אל by revelation ר ".
Jerusalem means "teaching of peace" and the New Jerusalem is the "new teaching of peace" ushered in by Christ when he said "You have heard it said... but I say ..."
The kingdom is like leaven/teaching.
Saved means "the flesh יע with a love for the increase of the word (teaching) ש."
The Hebrew word for 'marriage' also means 'doctrine'; so the bride are those who are taught by Christ.
Eating is a metaphor for learning, and the marriage supper of the lamb was the explosion of doctrine after the cross which revealed the mystery to the church.
'Born again' in Hebrew is to be 'yalad' again. 'Yalad' is the hand יד (a metaphor for work) with teaching ל at the heart.
If we restate the Westminster catechism, we might say that the chief end of man is is to know God, make him known, and give him pleasure; all through teaching.
The OP. Why should the church, past, present and future care about the epistles?
Some choose to believe that after the cross, God gave the NT authors special revelation to teach something new. This is implausible considering Paul's experience at Berea. He taught the Hebrews there his 'New Covenant' but they checked his doctrine and teaching against the Old Testament; the only scriptures they had.
Paul was teaching the sensus plenior of scripture; revealing the hidden mystery through the lens of Christ and the cross. The doctrine of Gospels and letters are derived from, and are a commentary on, the Old Testament sensus plenior.
When using the methods taught by the Gospel writers, and those revealed by the authors of the epistles, we not only eliminate the need for a Q document, but solve the Synoptic Problem.
For example, Notaikon is taught By John in 1 Jo 5:7-8, and Matthew in Matt 1:23. Paul teaches the use of metaphor in Galatians as he uses the two women as Grace and law. The hidden meaning of God is taught by the author of Hebrews as he shifts from milk to meat and the use of Melchizadek. John teaches the use of complex riddles in Rev 17 concerning the beast. All of these are based in the assumption that the literal history of Israel was used as a parable as God said it would be in De 28:37. It is a parable with the hidden meaning of Christ, the cross, and his bride.
The Q source is the OT itself when read for the sensus plenior. The differences between the Gospels demonstrate the increase of capability of the apostles to apply the teaching of Jesus to their OT studies. Mark began his story with the teaching of John. Matthew pushed it back to Abraham. Luke pushed the beginning to Adam, and John pushed it to Ge 1:1, deriving the doctrine of Jo 1:1-4 from the first three words of Ge 1:1. The Gospel are snapshots of their understanding at 10-15 year intervals.
The Epistles are teachings based in the understanding of the sensus plenior and using the techniques of it.
Together they give us what is needed to unpack the OT.
The methods of Sensus Plenior are derived from the NT authors use of the OT. Without these methods, scholars confess that they cannot read the scriptures the way Jesus and the NT authors did. (The result of a decade of debates concerning sensus plenior).