For a true anonymous group to work, even through email, we'd have toPerhaps something less than "true" would be less work, and cover most use cases, including Patti's.
I'm imagining that the "anonymous" feature could be available only to groups with Reply To set to "Group" (or "Moderators"). That would eliminate the need for forwarding emails (presuming you also remove the "Reply to Sender" footer link in such groups).
... a special, per individual, groups.io address, ...I think we'd still want this, but used in the From field, not as a Reply-To. Using a group address for re-written From fields is a mistake Yahoo Groups made (for DMARC support) and it can cause havoc with user's address books and address auto-complete mechanisms. As an individual (yet anonymous) From address it would be acceptable for this to be a no-reply address.
Possibly it could be built as a +member1234 version of the group's email address, where the 1234 would be a number unique to that subscription, such as the number used in the URL for their page in the Members list.
An advantage of forming it this way is that it might be forward compatible with a future forwarding mechanism.