No you're absolutely right and it's dumb as bricks.
Right now the only person who can delete a PM is the sender, not the recipient.
The recipient can mark it as read, but that doesn't help much.
Your local admin can do it for you in the database, for recipients local to the instance.
There currently is no way for a local admin to trigger federation of deletion of PMs sent to remote users either.
Although I think there's a Pull Request that implements the "removed" state.
I imagine that would trigger on bans that remove content.
I'm not sure if this will be exposed to users or just admins.