Maybe a little bit off the topic, but in some respects you already have a public inbox here:
If it also showed latest activity from others, it would be a perfect public inbox.
It might be better to have a separate tab for this public personal inbox though.
I hear you on this. Email notifications in general are a mess right now. The fact that people who want to get notifications from pre-upgrade conversations can't as well as the situation you've outlined where you do not have the ability to set the default to opt-out. We're dealing with a fragile situation right now where we can't rollout a fix until we can confirm it won't end up spamming everyone accidentally and/or suddenly dumping a backfill of notifications to some of the older community members who are tied to tons of content. The ability to control defaults for notifications is wrapped into this as well unfortunately.
Again, appreciate the feedback and letting us know in clear language the frustration associated with this.