When I joined the Eastern Orthodox church, I gained a different perspective on the mystery of Jesus' crucifixion and his suffering. Before, I'd looked at Jesus' suffering as an index of how severe our sins were and how much suffering was necessary for the Son of God to go through to balance our sin. Then I found that the early church looked at it differently.
In the writings of Athanasius of Alexandria, written in about 320 or 321 A.D., is a whole passage on the incarnation. In it, he talked about the mystery, the question of why Jesus had to die the way he did. What it comes down to is this: "The Son of God came to destroy the works of the devil" (1 John 3:8). He had to die in order to go into the lair, the domain of the evil one, the devil, in order to destroy the devil.
Theoretically, Jesus could have died by any means. Why couldn't he have died in bed? Why couldn't he have died of old age, or of an illness? St. Athanasius said that because Jesus was going into a contest against the evil one, he was like an athlete, allowing his challenger to choose the mode of contest. So Jesus didn't choose how he would die. He let evil be the one to choose.
And of course evil chose the very worst death that could possibly be. Athanasius said Jesus couldn't have died of old age or sickness, or all alone. It had to be a public death so people could see him die, and he had to be demonstrably dead so there would be no question that perhaps he just fainted and then came back. This was the will of God.1