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To me, it’s as if my daughter had died, is in heaven, but I would have no interest in the burial shroud that she left behind, mysteriously bearing her image.

In a way, yes. But different. I invoke this:

1 Timothy 1:4
or to devote themselves to myths and endless genealogies. Such things promote controversial speculations rather than advancing God’s work—which is by faith.

Christianity is unique compared to man made religions. For startes, there are no “holy” artifacts. A chuch is just a building. The body of believers is the real church. The shroud, if authentic, is just the cloth that wrapped the body of Jesus when he was dead. And I don’t give particular value to a bed if there is a sign on it that says “Lincoln slept here”, even if he really did.

For me, it is just an old cloth. On a related note, I’m REALLY glad Jesus didn’t pen any writings. Imagine what those would be worth. And imagine how they would cheapen the actual words in the writings.

IOW, it is not the artifacts that matter to me. It is Jesus and His word. I honestly do not care if the shroud is genuine or fake.

For startes, there are no “holy” artifacts.

Artifacts and relics aren't central to Christianity, but they have a place.

Once while some Israelites were burying a man, suddenly they saw a band of raiders; so they threw the man's body into Elisha's tomb. When the body touched Elisha's bones, the man came to life and stood up on his feet. (2 Kings 13:21)
When handkerchiefs or aprons that had merely touched his skin were placed on sick people, they were healed of their diseases, and evil spirits were expelled. (Acts 19:12)

Additionally, although the Shroud may not be important to your faith, scientists who have studied it have converted.