The way I see it, Jesus is peripheral at best, incidental at least to the whole matter. Consider.
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Pilate had from the time he was appointed Prefect taken a “my way or the highway” approach to the locals concerned. Putting standards in the Temple? Damn will do it and if the Jews don’t like it, they can jump into the Mediterranean. Using Temple funds to build an aqueduct? Hey, they are as Roman as Roads, and if I have to break a few Jewish heads to do it, I will. All these are attested in Philo and Josephus, the former only a few years after the event.
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Sejanus falls. Tiberius returns to the centre. Sejanus had been very notably anti-Semitic. Tiberius had said that the Empire was now going to be Judeophilic, if that’s a word. As the man in charge of the place with the most Jews, Pilate had to change his tune.
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And to rub salt in his wounds, the Jews complained to Tiberius about those damn standards and he sent back a letter telling Pilate to stop placing the standards in the Temple and start respecting Jewish law.. As related by Philo in that link.
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So how does this effect Jesus’s trial you may ask. Well, I think it’s clear that the Temple authorities were against Jesus because of theological reasons. And the only way they could get Pilate to sign off on the death sentence was to convince him that said theological reasons translated into security reasons.
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The thing is, Pilate’s room to overrule the Priests had reduced considerably as a result of events in Rome. All they had to say was “we’ll take this to Tiberius” and he has to start being more “reasonable”. Which, in the Gospel account they did and he was.
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Jesus’s guilt or innocence in Roman eyes was not the issue. The issue was the changed power dynamics in the region. He had to be a lot more careful about what battles he fought. He might have fallen out on some other issue and hell, probably did in the future.
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As you said, the fate of a preacher in Judea would not be an issue for Rome. Neither would the placing of Cohort standards. However, those things were emblematic of a different thing, fighting between Rome’s representative and their puppets, which was a matter for Rome.
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And one which had a very good chance of being decided against him, Rome would probably send back an answer along the lines of “seriously? Why are you interfering”.
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Are we really disagreeing on much?