After Lucifer and 1/3 part of the angels were cast out, I assume that Satan wanted to do everything he could to keep us from returning to Heavenly Father. It would seem to me that the best way to go about this would be to make sure that Jesus never died. If Jesus doesn’t die, then there is no redemption and we stay under the influence and aggravation of Satan. The better plan would have been to convince people that Jesus WAS the son of God at which point no one would ever touch him. So why didn’t Satan use his incredible gift of manipulation on man to keep Jesus alive?
The question you have proposed is a similar question I have asked myself, “If the Adversary’s desire was to thwart the will of God then why didn’t he (fill in the blank)”? The gospel plan appears to be contingent upon our Savior suffering in Gethsemane and being sacrificed on the cross; thus, by merely “[making] sure he never died” one would think this would be the best course of action for the Adversary to thwart our salvation/exaltation.
In relation to your question, we could even ask a similar question pertaining to Adam and Eve. If Satan wanted to keep us from returning to Heavenly Father, then why even tempt Adam and Eve to partake of the forbidden fruit? Why not keep them from eating the fruit from the tree of life? He didn’t however. He used his power of persuasion to tempt Eve and then used Eve to tempt Adam. Without Adam and Eve partaking of the fruit they would have lived forever and “they would have had no children.” The consequence of Adam and Eve not being able to have children would have clearly affected God’s work and glory“ to bring to pass the immortality and eternal life” of his heirs. The scriptures appear to be clear that he tempted Adam and Eve because “he knew not the mind of God.”
Within scripture we are also provided further insight into Satan’s character:
1) Moses 4:4:
“And he became Satan, yea, even the devil, the father of all lies, to deceive and to blind men, and to lead them captive at his will, even as many as would not hearken unto my voice.”
2) 2 Nephi 2:18:
“And because he had fallen from heaven, and had become miserable forever, he sought also the misery of all manknid.”
3) Moses 4:6:
“he knew not the mind of God.” As we contemplate these character descriptions two words stand out to me, “he sought,” the misery of all mankind — even the Lords.
The instant Adam and Eve partook of the fruit, the fall of man was successful. Humankind, those who were made in the image of God, relied (in totality) upon the bounteous love and mercy of Heavenly Father via the atonement. Satan, remaining constant, continued to seek the misery of all of the sons and daughters of Heavenly Father (because he knew not the mind of God). His ignorance appears to have lead him to believe that by causing the Savior to sin would be easier than having prevented the Savior from dying. This still would not have proved the Savior being the wrong choice since the Savior would have still been without sin. The Adversary, remember, believes he is God; he was supposed to be the Savior. If the Adversary was successful in tempting our Savior (Jesus Christ) to sin he then would have no longer been perfect providing no way for the sons and daughters to return to the presence of Heavenly Father.
In correlation with the previous paragraphs, Satan is the father of all lies and if he convinced the children of God that Jesus was the Savior then he would have been speaking the truth. If he spoke the truth, he would have been acting opposite to his character, because “there is no truth in him” (Source). Thus, it would appear, as a main reason as to why he couldn’t/wouldn’t teach others that Jesus Christ was the Savior is because he is unable to tell the truth due to the simple fact that the truth does not abide in him.