It is, therefore, likely that a member of the Jewish council asked Pilate for the body to be taken down, and entirely plausible that Pilate agreed. Whether it happened is another issue, but let us suppose it did - what happened to the body?
Pilate may have approved for the body to be taken down, but he did so to appease Jewish sensibilities, to avoid trouble. All that required was that the body was buried. There was no requirement for a proper burial, there was no reason for the Jews to do anything
On the contrary, the Roman's would have required that the body be buried dishonourably.
How The Jews Venerated Dead Saints and MartyrsAround the times of Jesus, veneration of dead prophets and martyrs was a big thing. As Jesus himself said:
Matthew 23:29 “Woe to you, scribes and Pharisees, hypocrites! For you build the tombs of the prophets and adorn the monuments of the righteous,Also consider the words of William Lane Craig:
"During Jesus’s time there was an extraordinary interest in the graves of Jewish martyrs and holy men and these were scrupulously cared for and honored."
How The Romans Cared About The DeadLike any other culture, the Roman's cared about how the dead were treated. More specifically with regards to executed criminals, the disposal of the body was a consideration.
For an example of a Roman denied honourable burial, we can look in the accounts of Suetonius, in The Lives of the Caesars:
For instance, to one man who begged humbly for burial, he is said to have replied: "The birds will soon settle that question."
More generally, this is from a site that describes itself as an "online evangelical encyclopedia of biblical Christianity":
The goal of Roman crucifixion was not just to kill the criminal, but also to mutilate and dishonour the body of the condemned. In ancient tradition, an honourable death required burial; leaving a body on the cross, so as to mutilate it and prevent its burial, was a grave dishonour for the victim.Crucifixion was the ultimate deterrent, and each part of it was designed to dishonour the victim - and that included disposal of the body
What The Romans Thought of JesusThe Romans accused Jesus of treason, and this was a very extreme crime - we know that because he suffered the most extreme punishment.
Jesus was welcomed into Jerusalem as a prophet, and the Romans would have been well aware that he had a big following among the Jews. I suspect this account is exaggerated, but it seems likely there were crowds welcoming him:
Matthew 21:8 Most of the crowd spread their cloaks on the road, and others cut branches from the trees and spread them on the road. 9 And the crowds that went before him and that followed him were shouting, “Hosanna to the Son of David! Blessed is he who comes in the name of the Lord! Hosanna in the highest!” 10 And when he entered Jerusalem, the whole city was stirred up, saying, “Who is this?” 11 And the crowds said, “This is the prophet Jesus, from Nazareth of Galilee.”Jesus was crucified to stop any chance of him leading the Jews into revolt. Christians might argue that that was not Jesus' way, but it does not matter. The Roman's perceived him as a rebel leader, and we know that because he was executed as a rebel leader:
Matthew 27:37 Above his head they placed the written charge against him: this is Jesus, the king of the Jews.In fact many Christians will say Jesus was executed for blasphemy, but that is not true. The Roman's did not care about blasphemy against the God of the Jews.
How The Romans Would Have Dealt With JesusThey crucified him as a rebel leader, and the last thing the Roman's wanted was for Jesus to be a martyr, to be a symbol for rebellion after death.
It would have been a very real possibility that Jesus tomb would be venerated, given he was hailed as a prophet by at least one segment of the Jews in Jerusalem (despite the sanhedrin conspiring against him - if that even happened). Would the Romans want the tomb of a man executed for treason to be venerated? Absolutely not!
The Romans may well have permitted the body to be taken down, but it is inconceivable that they would have allowed an honourable burial for him.
I find it odd how Christians cite the historical evidence for crucifixion victims being taken down from the cross, but ignore the historical evidence for them then being buried in dishonour. Cherry-picking at its finest.