OK, but the Gospels do teach the NT, right? Jesus preached the New Covenant. Maybe I'm not understanding where your point leads.
The Body of Christ, however, benefits from the spiritual blessings of the New Covenant by way of regeneration and acceptance with God (reconciliation), adoption and sonship, by virtue of that same shed Blood. This is the special connotation of “NEW TESTAMENT.”
The Body of Christ is not a subject of revelation in the Gospels, but a subject of special revelation in the Epistles of Paul.
It is correct to draw spiritual application from any place in the Scriptures, including the Gospels. But as revelation is progressive through the Scriptures, it is important not to appropriate doctrines from a previous dispensation that are peculiar to God's dealing with Israel as a nation.
Spiritual applications from the Beatitudes (Matthew chs. 5 through 7) are not only acceptable, but should not be avoided. Where specific instruction in those chapters appears to be inconsistent with the Pauline Epistles, however, one should be very careful of a dispensational change in order and instruction.
The spiritual principles of the Beatitutdes, binding on the members of the Body of Christ, are re-enunciated in the Epistles. It is not difficult to recognize them.