From the Gospels it doesn’t seem that the Romans were paying much attention to Jesus, or that he was encouraging violence against the Romans. The Jewish leaders had to portray him to Pilate as a threat to Roman rule. Crucifixion was a Roman method of execution. Why didn’t the Jewish leaders try to have Jesus stoned to death like they later did to Stephen? Probably they didn’t think they could get a crowd to do it.
Jews are not allowed to kill, especially on passover so they had to have the Gentiles do it.