I mean, he was not a canonical prophet (nothing he wrote was included in the biblical canon), but it's interesting that he brought a message of rebuke to a canonical prophet.

Crater,

You touched an important point.

"David had committed a grievous sin, toward both Uriah and Bathsheba... Though there would be found none in Israel to execute the sentence of death upon the anointed of the Lord, David trembled, lest, guilty and unforgiven, he should be cut down by the swift judgment of God. But the message was sent him by the prophet, 'The Lord also hath put away thy sin; thou shalt not die.' Yet justice must be maintained. The sentence of death was transferred from David to the child of his sin. Thus the king was given opportunity for repentance; while to him the suffering and death of the child, as a part of his punishment, was far more bitter than his own death could have been. The prophet said, 'Because by this deed thou hast given great occasion to the enemies of the Lord to blaspheme, the child also that is born unto thee shall surely die'" (PP 722).

Yes I agree, that is interesting.

Apparently like some of the other OT prophets, Nathan didn't take up the pen and write, yet some of his spoken words were recorded in scripture.

Neither did Jesus. Is He canonical? He wrote in the sand, but we do not have the words He wrote.

In fact, he produced writings (1 Chron. 29:29, 2 Chron. 9:29), but they apparently weren't included in the canon. So he and other prophets, like Gad, Ahijah, and Iddo are literary but non-canonical prophets. Ellen White is also included in this category.
The fact that a non-canonical prophet brought a message of God to a canonical prophet shows that there are no degrees of inspiration or authority.

Interesting,

Though not included in the cannon are any of the mentioned bools or writings in existence today?

No, they aren’t in existence today. We don’t know if those books and the writings of other non-canonical literary prophets still existed by the time the OT canon was formed (perhaps 400 B.C.); therefore, we do not know if their exclusion was a deliberate decision on the part of the compiler(s), or if there was no choice because the books had already been lost.

Does this mean that the sentence of death, in general, can be passed around?

This is a good question, Arnold. Did the young child become David´s savior? A substitute or a peace offering?

You guys certainly do have an interesting discussion going on here!

I am also scheduled to present the lesson study in our church this coming Sabbath.