The shortest answer I can think of is that Jesus is both the fullest revelation of God and the revelation for our time in history. We have the testimony about Christ - that is the message God has ordained until the end of the ages.
Hebrews 1:1-2 - Long ago, at many times and in many ways, God spoke to our fathers by the prophets, but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world.
Some questions that might accompany that thought:
In what ways is Jesus’ life the greatest revelation mankind has received?
How has Jesus fulfilled the promises of the OT?
According to Jesus, what is the next stage in God’s revelation to mankind?
If, as @Jimmy_Sellers pointed out, part of his concern is that the Bible does not address modern questions, you might ask:
What is necessary beyond love God and love neighbor? How come you feel the need for the advice to be more specific?
In Paul’s letters to the Churches he addresses many issues we face in modern culture - in fact, many of the very same issues - sexuality, relationship to governing authorities, gender issues, taking care of the poor among us. What do you feel is lacking from Paul’s letters? What do you think a ‘letter to the citizens of New York’ would contain that would be different than the ‘letter to the Corinthians’?
One further thought after reading your reply:
No more books of the New Testament have been written because all of the eye witnesses of Christ have died. The NT was written by those who saw Jesus and experienced His life, death and resurrection or whom God called (like Paul) to be a witness while the eye witnesses still lived and could verify what was being taught.
So, no more is written because the eyewitnesses of Jesus, the fullest and final revelation of God to man until the end of ages, have died. That was one of the tests for canonicity - if the author walked with Christ (literally - on earth).