Exactly right. In fact, Zarr can make it even harder to copy, because now you have millions of small files instead of a few large ones. What I currently do is just write chunked data (N5/Zarr) directly to a final destination directory and plan on never moving or copying it.
This is supported by Nextflow’s symlink staging method, but when creating the Zarr you have to input the parent directory for the Zarr container separately from the container name, so that the parent directory gets linked into the process dir and mounted into the container.