Understanding human nature and all the baggage we carry can go a very long way to understanding this story in its historical context. Jewish religious leaders (during a particular period of political weakness and religious uncertainty) were both worried about the Finger Pointer's impact on the Judeans causing Rome to crack-down, and on Jesus having become more popular than them. They "conveniently" put aside in their own minds the tacky irksomeness of the second issue for the high-minded concern of the first issue. If they were stronger in popularity, character and faith they would not have done it. (It was as if a ram had never been provided Abraham to spare Isaac -- specifically, innocents are not to be sacrificed for the guilty.)
But their reaction is understandable. It's a natural offshoot of any who are in position of authority and fearful of losing it.
What they did was in keeping with the patterns of their Roman overlords. They employed a very Roman method for ridding themselves of both problems. No, I don't mean the crucifixion, I mean employing a mob to make it appear that Jesus' removal was widely popular.
Now, next, is a very important element to consider. What is so smarmy about Pilate's role in all this, and normally ignored, for it depends a good deal on how one reads the words of the gospels, and it is very helpful to know Roman history when you do.
First off, Pilate certainly knew (just as most of us today could not know unless we studied Roman History) how Romanesque was the mob which demanded Jesus' execution.
It was thru the employ of the mob that Rome herself had been transformed by politically astute and ambitious schemers from a Republic (that thoroughly hated Kings) to a Dictatorship.
Since the Roman Emperor continued to cultivate its own rabble in order to retain control, Pilate almost certainly knew the Jewish Priests were following the Roman pattern. It can be read that he was needling them with his "But this man has committed no crime. I can see no guilt in him." After all, it is Jewish law which centers itself around God-based morally, not the whim of an Emperor. In light of this, I think anyone could see that Pilate's comments were quite urbane and cynical, a proudly Roman tradition by this time.
Those who despise the United States have been trying to use mobs to undermine us too. A good reason to suppress knowledge of the Bible and any of its stories, not just this one, is the same reason history courses have been revised. A populace unfamiliar with history is more easily led down old roads to enslavement.