I was wondering, why might Jesus not have stated the Old Testament canon in something like a list, and instead let others take account (define and compile) for that canon?
Why should he have needed to? He spoke to clarify doctrine and correct mistakes. He didn't define what books comprised the scriptures for the same reason he didn't define what a fig is when he mentioned figs: because the people he was talking to already had a clear understanding of the matter.
Christ provides the bookends of the Old Testament.
That the blood of all the prophets, which was shed from the foundation of the world, may be required of this generation; From the blood of Abel unto the blood of Zacharias, which perished between the altar and the temple: verily I say unto you, It shall be required of this generation. Luke 11:50-51
We are all familiar with the first death of Abel, but who was Zacharias? To answer this, we need to know that the Old Testament structure in Jesus' time began with Genesis and ended with 2nd Chronicles.
The Book of Chronicles (Hebrew: דִּבְרֵי־הַיָּמִים Dīvrē-hayYāmīm) is a book in the Hebrew Bible. Chronicles is the final book of the Hebrew Bible, concluding the third section of the Jewish Tanakh, the Ketuvim ("Writings"). It contains a genealogy starting with Adam and a history of ancient Judah and Israel up to the Edict of Cyrus in 539 BCE. -wiki-
In Chronicles 24:20-22, we find the final death of a prophet Zechariah.
And the Spirit of God came upon [this is a reference to operating as a prophet] Zechariah the son of Jehoiada the priest, which stood above the people, and said unto them, Thus saith God, Why transgress ye the commandments of the LORD, that ye cannot prosper? because ye have forsaken the LORD, he hath also forsaken you. And they conspired against him, and stoned him with stones at the commandment of the king in the court of the house of the LORD. Thus Joash the king remembered not the kindness which Jehoiada his father had done to him, but slew his son. And when he died, he said, The LORD look upon it, and require it.
So, with that information, we have the beginning and ending of the Scriptures.
Additionally, also in Luke, we have Christ outlining the same three categories of law, prophets, and psalms.
And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.
The confusion over the books of the Old Testament arose afterwards as some believed the writings between Ezra, author of Chronicles, and John the Baptist were inspired also. This is odd because Maccabees itself claims there are no prophets at the time of its writing.
Extant copies of the Septuagint, which date from the 4th century CE, contain books and additions not present in the Hebrew Bible as established in the Palestinian Jewish canon and are not uniform in their contents. According to some scholars, there is no evidence that the Septuagint included these additional books. These copies of the Septuagint include books known as anagignoskomena in Greek and in English as deuterocanon (derived from the Greek words for "second canon"), books not included in the Jewish canon. -wiki 2-
Peter also points to the authority of God moving people to write as the key requirement.
For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost. 2 Peter 1:21
So, to answer the OP, Jesus and the others knew what was Scripture and what was not and why it was Scripture, even if others disagree.