Oh, woah, that’s an interesting leap. I’m not sure I agree, actually, but I think I get the logic. Have to think about this one…
I think there are a lot of existing design models for this, and few that I can think of intermix direct/private and group. Slack doesn’t, neither does Discord. Telegram does, but I find it quite disorienting. 
I suppose in a way what you’re talking about is a more email-like model, actually. Would you agree? Where there is not necessarily a different feed or inbox or anything for 1:1 vs. “group”. That said I think the context of email is generally fairly different from that of a forum, with the balance leaning pretty heavily toward “most of this is directly relevant to me/relevant only to me” in email, whereas in a forum it is often much more “a lot of this may not be relevant to me”, and a PM is absolutely relevant to you. So mixing it in to some feed where not every message even “includes” you explicitly seems odd… And putting it into some view of only subscribed topics or something seems like a recipe for it not getting seen or, at the least no different/no better than just treating PMs as you do now… 