I've thought some about this topic before but this discussion motivated me to try to put some of these together to try to get a bigger picture. Here are some related to this discussion:
In connection with Satan the Devil killing others:
Jesus called him "a manslayer when he began." (Jn 8:44)
The apparent reference is to his actions in the garden with Adam and Eve.
The Genesis account shows he was "a manslayer" by prompting them to sin, rather than by directly killing them.
Hebrews 2:14, 15 describes Satan as "the one having the means to cause death" and others being in slavery (to him) due to "fear of death."
I mention these two things because they seem to support the idea that Satan benefits more from having live subjects rather than dead resistors. At the same time, the threat of death would be a useful tool, perhaps used on some to affect the many.
In connection with Satan knowing that Jesus' death would be his undoing (and thus, why kill him?)
From what I can see, God knew ahead of time the details of how and when Jesus would die and systematically withheld that information from Satan (and others for that matter).
Prior to the flood (of Noah's day): God promises a savior (Gen 3:15), curses the ground, eventually many angels sin, the flood wipes out the preflood world, the curse is lifted, mankind starts anew, no further record of any angelic defections. And no more information about the coming Saviour until after all this happens. Effectively eliminating the possibility of any angels learning the details and then turning bad.
For the period after the flood, 1 Peter 1:10 - 12 indicated the prophets could not fully grasp what they were predicting about the Messiah, nor could angels.
Eph 3:8 - 10 also states these things were hidden by God only to be explained by the Christian congregation (after the fact).
Luke 18:31 - 34 and Mark 9:30 - 32 give examples of Jesus' disciples being unable to grasp details of Jesus' death, saying they were purposely "hidden from them."
From this and the above I gather (so far anyways) that Satan would have been more pleased to break Jesus' integrity to God rather than to kill him. But at the same time, the significance of Jesus' death was kept from him.
Another thing that I gather from the fact that humans are held accountable by God despite pressure from Satan is this: That Satan is not in complete control. That is to say, he could incite great opposition to Jesus with the hope of breaking him, but not be able to prevent the momentum of that opposition from killing Jesus, which is exactly what God wanted to happen. Further, the accounts show that Satan recognized who Jesus was. So Satan would see that Jesus was the key person to break, motivating him to go 'all out' as it were. It's as if Satan was given just the right amount of information to cause him to act in a predictable fashion.
Incidentally, Jesus appears to have understood why and when and how he would die based on numerous statements of his.