I don’t see the problem. The burial shroud is a “by-product” of his crucifixion and burial and (depending on how one interprets the image) his resurrectionl. I don’t see it as an question “should I leave this behind me or not.” He suffered, died, was buried, and rose. In the process of burial a shroud was used. That it became imprinted with this image is a consquence. We don’t know how the image was produced, whether it actually suggests some unique process associated with resurrection or whether it’s “just” the result of burial. But either way, it’s just what is. I don’t see this as Jesus asking himself, “should I or shouldn’t I.”
I don’t think it’s helpful to puzzle over that question.
Uhhh ... Jesus Christ is GOD!!! You know ... "second" Person of the Holy Trinity? Through whom all things came to be?
If(!) the shroud is really His burial cloth ... then it exists because He wants it to exist. He made it that way ... nobody else did. If He had wanted it to vanish ... it would have vanished.
Scripture records that His burial cloths were still in the tomb ... and even records the manner in which they were left.
I don't think that's something to take lightly.