Sorry, but that example you found there is the implementation of a dereferrer and would not hide the referrer when clicking e.g. on that external link you just posted except if you had manually added the https://www.example.com/hide-referer? part in your post.
And if that is true, then thank you for pointing that out. But my point still stands that there are options available that do not require the need to make a substantial edification to the source code (hence, the work, the time for that) for this specific feature.
You already pointed out a way to do it using an existing feature (and thank you for doing that; I appreciate it as I too wanted outbound links scrubbed). If others want that, they surely would come to Meta and search for it.
You are welcome to submit a PR for it, or build a plugin. That is what those options are there for.