In Matthew 12, Jesus states three times that “something greater than _____ is here.”
First, he says in Matthew 12:6 that
I tell you, something greater than the temple is here.
Second (and third), he says in Matthew 12:41-42 that
The men of Nineveh will rise up at the judgment with this generation and condemn it, for they repented at the preaching of Jonah, and something greater than Jonah is here. The queen of the South will rise up at the judgment with this generation and condemn it, for she came from the ends of the earth to hear the wisdom of Solomon, and behold, something greater than Solomon is here.
So, Jesus is greater than the temple, Jonah, and Solomon.
He’s greater than the priesthood (the temple), the prophets (Jonah), and the kings (Solomon). Each of these Old Testament offices pointed to something greater than themselves, and the Greater-Than One is now here.
This is one of my favorite passages precisely because of the reasons you listed above.