I admit that this is a troubling problem with the position that I stated, but I don't think it's a complete takedown.

The easiest rebuttal would be to simply say that continuity is not a mere implementation detail. If you give up continuity, you can make a copy without altering the original, you just have to read it.

But if you need to ensure continuity you have to alter the original. This seems to me a very fundamental part of the process, making it qualitatively different.