Actually, I'd say that, on the contrary, it fits another overdone kind of relic.
You know the kind of slapstick cartoon where someone gets a hot towel or such slapped on their face, and when pulled off, their face is on the towel? Screwball Squirrel did it to the dog, for example. And I'm pretty sure Woody Woodpecker does it at least once, and Foghorn Leghorn does it once to the dog too.
Well... Xianity has an apocryphal story where exactly that happens to Jesus. A woman offers him a cloth to wipe his face while he's carrying the cross, and the image of his face remains printed on the towel. (And yet somehow none of the gospel writers ever heard about such a conspicuous thing happening right in the middle of the whole crucifixion event.)
Seriously, you know it's sophisticated enough theology when it's indistinguishable from a slapstick Tex Avery cartoon
While the story is not canon, such Jesus-onna-cloth relics were incredibly popular, especially in the Eastern Orthodoxy. And both halves, although again more the eastern Empire had a whole craze of paintings of Jesus just "appearing" on some canvas by miracle. And they had plenty of those, oh, about 1000 years before the shroud.
And I don't even mean the underground kind of popular. Emperor Heraclius actually used such a "miraculous" Jesus-onna-cloth image as the battle flag to inspire the troops. You can't get more mainstream than being the emperor's battle standard, really.
The shroud seems to me like just taking that to the logical conclusion. If people are willing to venerate a piece of cloth with Jebus' face on it, and pay big money for it, how much would a full-body image sell for? I strongly suspect that someone back then found the answer to that question.
Now we also know that those faces on a towel can't all be true, because they don't even look like each other. Nor like the face of the fellow on the shroud.
Which brings me to my question for Jabba: so how do you know YOURS is the real thing? Do you have any chain of custody to show its origin? Even if we were to concede the blood and the weave just for lulz, can you show that it's not the shroud of BRIAN instead of Jesus?