That's a nice way of putting it and it definitely resonates with my experience.
But why wouldn't it be possible to have these two in the same app as long as they are very cleanly separated in terms of who gets to notify me when, what's displayed where etc.?
WhatsApp (with channels) and Telegram (with its huge groups) seem to address both just fine, as far as I can tell, although I barely use their "mass-messaging/social-media-like" features.
As to whether one protocol can address both use cases: Maybe it doesn't need to either? I could see 1:1 chats and "ephemeral/barbecue" groups using one type of history persistence policy (i.e. usually none) and large group chats/pub-sub-like feeds another. This could all be independent of what holds somebody's persistent identity/identities.