Creating a hard link to an ordinary file returns an error. What could be the reason for this?

Hidden files (prefixed with a dot) are valid hard link sources; the hidden attribute only affects default directory listing visibility.

Read-only permissions on the source file do not prevent hard link creation, because the operation modifies the directory entry rather than the file's data or metadata.

Shell scripts are ordinary files and can be hard-linked without any restriction.

A file that is already a hard link (link count greater than 1) can still receive additional hard links, as all directory entries pointing to the same inode are treated equally by the filesystem.

Hard links work by creating an additional directory entry pointing to the same inode as the source file, but inode numbers are local to and only meaningful within their own filesystem. When the source and target reside on different filesystems (for example, / and /home on separate partitions), the kernel cannot create a valid inode reference across that boundary and returns an 'Invalid cross-device link' error.