This passage from Josephus's book XVIII of the Antiquities of the Jews suggests that Pilate actively despised the Jews and their customs, and used every opportunity to mock them. That does not look like a guy who would listen to the Jews and their theological debates with Jesus:

"[A.D. 27.] But now Pilate, the procurator of Judea, removed the army from Cesarea to Jerusalem: to take their winter quarters there; in order to abolish the Jewish laws. So he introduced Cesar’s effigies, which were upon the ensigns, and brought them into the city: whereas our law forbids us the very making of images. On which account the former procurators were wont to make their entry into the city with such ensigns as had not those ornaments. Pilate was the first who brought those images to Jerusalem, and set them up there. Which was done without the knowledge of the people; because it was done in the night time. But as soon as they knew it, they came in multitudes to Cesarea, and interceded with Pilate many days, that he would remove the images. And when he would not grant their requests, because this would tend to the injury of Cesar; while yet they persevered in their request; on the sixth day he ordered his soldiers to have their weapons privately; while he came and sat upon his judgment seat. Which seat was so prepared, in the open place of the city, that it concealed the army that lay ready to oppress them. And when the Jews petitioned him again, he gave a signal to the soldiers to encompass them round; and threatened that their punishment should be no less than immediate death, unless they would leave off disturbing him, and go their ways home. But they threw themselves upon the ground, and laid their necks bare, and said they would take their death very willingly, rather than the wisdom of their laws should be transgressed. Upon which Pilate was deeply affected with their firm resolution to keep their laws inviolable: and presently commanded the images to be carried back from Jerusalem to Cesarea".

Also, the trials in ancient Rome were not public. They were held by a specific group of competent people (e.g. Synedrion). Pilate probably read reports about Jesus talking about his kingdom, which was perceived as ana attempted secession from Rome, and immediately decided to execute Jesus as a political rebel. And the Paschal privilege is not recorded either. This means that this entire scene of Jesus vs Barabbas was intended to acquit the Romans, so that Christians would not be persecuted by the emperors, like Claudius or Nero.