Why Pilate? Because of the Roman persecution of the name "Christiani" per se

[Giuseppe]

The Eucharist had introduced the distinction between a before and an after of itself as a particular event. The crucifixion of Jesus couldn't longer be considered as out of the space-time (and therefore both before and after the Eucharist). It had be placed in the historical past.

Since the Eucharist insists (by definition) on the reality of the flesh and blood "that is given for you",...

...And since the real flesh and blood of the Christians was shed in abundance during the early Roman persecutions of the name "Christian",...

...then the name was found (via Josephus) in Pilate as of the Roman persecutor par excellence, perfect protoype of all the late persecutions, by Roman authorities, of the Christians as Christians

In other terms, Pilate had to crucify Christ as Christ because it was strongly expected by the Roman authorities precisely the punition of the Christians as Christians.

The idea was so diffuse (about the Roman opposition to the name of Christiani) that even Tacitus accepted acritically the idea that the killer of "Christ" could be only and only a Roman authority: Pilate.

[Giuseppe]

Hence the Barabbas episode serves to point out again and again the fact that Pilate crucified Jesus as THE Christ, and he crucified not Jesus as simply "Jesus" or as "Son of God (Father)" or for other reasons different from the title CHRIST being given to Jesus.

The reader had to be secured that the Romans were involved in the crucifixion insofar the condemned Jesus was named "the Christ".

Just as the same Christians were persuaded that they were persecuted by the Romans only in virtue of their name: Christiani.

Hence the martyrdom doesn't prove the historicity of the Jesus ("who would die for a lie?") but rather the contrary: the martyrdom proves why the idea had to be invented, of a Pilate killing Jesus.