Not possible to copy record when missing read access on xxx2Many records
I don't know if it will be a good feature or not.
But ModelStorage.copy read all the fields of the records so if the user doesn't have read access to some fields or xxx2many records than the copy will fail.
A possible solution will be to read without check access.
Another solution will be to let the developer set default value for those fields and read only the field that we need.