We can do this by providing a download for a OPML file.
Perhaps better than allowing simply the download of an OPML file, it would be nice to have the ability to provide a link to an OPML file as well? This way feed readers like Inoreader that support OPML subscription would be able to auto update themselves when new feeds/friends are added to the list?
Depending on your infrastructure, you could potentially leverage the old Link Manager within WordPress which provided OPML outputs as well as outputs arranged by category. This would prevent you from needing to rebuild the side-files unless you’re doing that already.