@Puzzleannie: Yes, it would seem that Christ humbled Himself in all ways to experience the full spectrum of human life. Hence Him working with St. Joseph as a carpenter, and the things that Salvatore123 said. To me, your ideas would go towards the Catholic concept of penance and indulgence. By this I mean that even though when we are forgiven, we still deserve temporal punishment. Just as even though Christ’s redemption ensured the eventual restoration of the universe, currently its’ restoration is spiritual, and humanity is tasked with aligning the world with Christ’s redemption. Even though Christ and the Blessed Virgin were both fully free from original sin in body and soul, they lived in a world with natural sin in it, thus their own purity did not automatically purify the world around them - unless through a miracle, as you noted, which was primarily for faith, not to exemplify His lack of original sin, which was proven simply by His completely sinless life, even the unintentional habits we pick up.
@Salvatore123: Those are very good points, I hadn’t thought about it from the angle of His redemptive mission, though I think it had been part of my speculation. I had the image of Christ being killed by a disease or a random boulder falling on Him, thus ending His mission due to complete randomness. However, I think it is also quite plausible that God assured His safety, but let Him remain “humbled” by experiencing the natural sin that we all experience, evidenced by the trials you noted.
@Hecares: While He was without personal sin, He also lacked original sin too, so “without sin” must include both personal and original. To more fully reply to your points, see my responses above, which deal with some similar ideas.