As I understood it's because we can't move root to another page.
Actually not. Path to node could change completely, For example, for page on second level path is 0-234 (where 0 is a root page, 234 is a page on second level). After root split path will be 0-new_page-234.
If algorithm could be able to change root then new path could be looked as new_root-new_page-234 because old root could be splitted to old_root_page and new_page.