Jesus came to die (to be killed) as a sacrifice for our sins. So didn’t someone have to kill Him? And even if everyone had responded to Jesus in the right way (as, for instance, the apostles did), wouldn’t Jesus still have needed to be killed? After all, Jesus came to die for His apostles just as much as He did for the Jews and Romans.
The question seems to put the emphasis on the Jews and Romans’ decision to kill Jesus. I would say the emphasis should be on Jesus’ willingness to lay down by his life on his accord: "No one takes it from me, but I lay it down of my own accord. I have power to lay it down, and I have power to take it again; this charge I have received from my Father” (John 10:18).
With that said, we can say that God willed to bring about the greatest good ever from the worst evil ever–namely the salvation of the world. It is similar to the Easter Vigil’s "O Happy Fault that merited such and so great a Redeemer!” The salvation that God brings to the world through the death of Jesus manifests his power. There is no evil, no matter how grave it may be, that is not permitted without it contributing to God’s overall plan of salvation.
So, did the Jews and Romans do us a favor in killing Jesus? I think the question is framed wrongly because it makes it sound like the Jews and Romans did a good thing. They did not. Perhaps the question should be framed, “Did God bring about a greater good from the evil actions of those that killed Jesus?” The answer is yes.