Because the authors thought Jesus would return at any time. They didn't write it down because the didn't see the need. As they aged they changed their minds and penned the eyewitness accounts.
Why no accounts written contemporaneously with, or shortly after Jesus?
Answered above. What were you doing on September 11? Where were you? How did you first find out?
And with that time delay, doesnt that imply a 2nd- or 3rd-generation telling of the story
No. Jesus was crucified at 33. If an eyewitness was 23 when Jesus was nailed to a cross, he would have been 73 at the 50 year mark.
If I might add, one reason we know the accounts that were written were accurate is because they were read by people who actually lived through the events. The NT testament closed with the death of the last Apostle, John.