That would explain the date of 1 century, but it would not explain the photographic (for lack of a better word) nature of the Shroud:
No pigments, paints, dyes or stains were found on the fibrils of the linen cloth. It is not a painting. An image analyzer shows the Shroud has a unique, three-dimensional codex embedded in it, unlike any other two dimensional image made by humans. While some explanations of what caused the image on the Shroud are possible from a chemical point of view, there are precluded by physics and certain physical explanations are conversely completely precluded by the chemistry. To explain the Shroud image there must be a complete explanation from a physical, chemical, biological, and medical standpoint. To date no one has presented this complete solution. It is an enigma.The best scientific explanation is that the Shroud image was produced by something which resulted in “oxidation, dehydration and conjugation of the polysaccharide structure of the microfibrils” of the linen itself. STURP concluded that for now that the “Shroud image is that of a real human form of a scourged, crucified man. It is not the product of an artist.”
If the headcloth was placed about the head, then removed (before the large cloth was wrapped around the body), and then wrapped up and laying in a separate spot by the preparers, then why would John write about that particular fact as though it was a surprising part of the whole shocking scene?
Why wouldn't he? It is evidence, so he described it.
I would believe, that as we do today, Jesus' face and head was covered just after He was removed from the Cross and He was transported to the Tomb. Therein as preparation for draping Jesus with the Shroud, it was removed and set aside, and His eyes covered with coins. I believe Jewish funerary rites require that the body of a decedent be buried as soon as possible after death, but the coming Sabbath would not allow for the full completion, hence the planned return thereafter.
Thank you all for the interesting commentaries.