Those who have placed their faith in Christ don't need the shroud to confirm the One in whom they have placed their faith.
Those who have chosen not to place their faith in Christ will reject that the shroud was Jesus' no matter what evidences may be presented.
What about a doubting Thomas? I know of specific examples that refute your third point, though in large measure you are right.
The Shroud is not meaningless.
Dan
Just because people should not base their faith on the Shroud (though I think if a non-Christian can overcome his doubt through the Shroud and take the first step through the door because of it, that is not a bad thing) that does not make the Shroud un-important.