Per MDN, Referrer-Policy isn't supported in IE/Edge either, so you'd have to do browser sniffing. This seems like it has the potential for something to go wrong and cause a referer leak.
On the other hand, if it's a public site then obviously there's no concern about the URL leaking, so I'd think this should only be turned on for sites that are set as private.
I'm guessing that the underlying problem here is that you can share things in Google Drive / Google Docs to "anyone with the link" and when that's enabled, you probably didn't actually intend to share it with the owners of the websites that you happened to link to. Safer to just never let the URL leak.
On the other hand, if it's a public site then obviously there's no concern about the URL leaking, so I'd think this should only be turned on for sites that are set as private.