Actually, Jews could have cared less whether he lived or died. There are primary source documents of letters back and forth within the Roman Empire talking about getting Jesus killed.
First, because the Romans adore tradition. They hated anything new, especially Religions. And what Jesus was doing was very upsetting. He was also getting a following which the Romans didn't like, either.
The Romans and Jews depicted in the Passion of the Christ is... Heh, blasphemy.
Perhaps Jesus was the OG ANTIFA/SLM (Sinners Lives Matter, not to say BLM *is* SLM, this is parody) and the government made him a scapegoat and rallied the populace against him.