Features
Host the file, repoint the code
Upload the PDF, the image or the menu, and point a code at it. When there is a new version, upload it and repoint — the printed code never notices.
Why not link to a file on your own site
Do, if it will stay where it is. In practice files move when a site is rebuilt, and a printed code aimed at a file path is the most fragile arrangement there is. Hosting it here means the address is one we control and the code points at the library entry rather than a filename.
Versions
Replacing a file replaces what the code serves. The old one is not left lying around at a guessable address afterwards.