First, it wasn't in Satan's power to "let Jesus live" or not. Jesus plainly said that He Himself had the power to lay down his own life and take it up again, and that no one else could take it from him.
Second, if Jesus had lived he could then only do as his new master ordered, even if he was put in charge of the whole world.
Third, Satan's doom was sealed the moment he chose to rebel against God, and he knew it. His purpose in temptation was not to rule the world, but to keep Jesus from redeeming mankind, thereby hurting God the only way he could.