It is An overused SSS level magic item.
Mr. Weasley had said to be wary of anything that thinks but you can't see where its brain is. He was referring to the diary. Sure enough, a small diary turned out to be one of the Horcruxes, and almost completed the task of restoring Voldemort's youthful body on its own.
The Sorting hat is no more innocent than that diary. The origin of the Sorting hat was a disagreement between the school's four founders over student standards. Slytherin opposed all non-pure-blood, while Hufflepuff admitted everyone, while Gryffindor and Ravenclaw each selected people who matched their attributes, courage or intelligence, regardless of origin.
If we were to enlarge Hogwarts as a society, there would be no doubt that Slytherin represented the noble class with a claim to blood, Hufflepuff the common class, Gryffindor the chivalrous class with a pride in valour, and Ravenclaw the scholar class with a pride in intelligence. Since Slytherin is the only one who can claim birth, he pits himself against the other three founders, and Slytherin leaves. This corresponds to the historical struggle of the non-noble classes to overthrow the aristocratic structure. It is said that the four elders created the sorting hat out of fairness.
But given the class antagonism mentioned above, the seemingly neutral sorting hat, which divided people fairly into houses, was not really neutral. It's probably loaded with a plugin against Slytherin by the other three Senators. For example, the Sorting Hat's songs have always been about the individual houses. But in the fourth year, when Voldemort came back from the dead, it suddenly changed its song for the first time, calling on everyone to unite and defend the school. Voldemort is a Slytherin descendant and a Slytherin graduate, and if he ever rules he will naturally be cleansed of pure blood according to Slytherin's philosophy.
For a neutral hat, the change is neither good nor bad. However, the hat showed a very high tendency to warn people not to let this happen. So this hat has at least two qualities. First, it can predict a crisis accurately, which only a handful of people or things in the wizarding world can do.
Second, it is not entirely neutral; there is a clear bias against Slytherin. On this second point, there is evidence that the sword of Gryffindor, used by Neville to kill the Horcrux Nagini in Episode VII, was drawn from inside the Sorting Hat. So the Sorting Hat actually participated in the Battle of the Castle, providing prophecy and effective weapons for the Inverts. Nagini would be difficult to kill without the Sorting Hat's help, and Voldemort's chances would be greatly enhanced.
So it's possible that the Sorting hat was a spy-like object that the three Elders deliberately planted in the castle. No one would think of getting rid of it because of the necessary sorting work and the lack of movement. But the purpose of the hat was to do something about it, whether it was to give a warning or to give a superior weapon, if the Slytherins seemed to be on the point of raising their heads and subverting the existing order established by the G-la-Heh.
So the Sorting hat was actually a seemingly insignificant weapon that the three Elders had planted inside the castle to ensure that the Slytherins could never fight back. As far as sorting was concerned, I thought the Sorting Hat's procedures were roughly fair, such as the detection of fragments of Voldemort's soul in Harry and the argument for placing him in Slytherin.
But we can't rule out that the three elders have some small thoughts in it. Think, for example, of some of the lopsided people at Hogwarts who never behaved positively: Crabbe, Goyle, Parkinson, all of whom were put in Slytherin.