Except for “not really new bumps” such as a late last post in the topic edit, the highest post id would be the that of the last post in the topmost Latest topic.
A problem being the posts in messages and other not-visible topics also get post ids.
So the easy solution of setting a cookie with that number to use in subtracting from the next visits highest post id wouldn’t really be accurate enough.
Similar for topic ids.
Thus any of the “easier” approaches that I can think of would be flawed over-estimates at best.
I do think it would be possible to have a plugin use custom fields tied in with login so that a type of “there have been n new posts” could be possible.
But I have to wonder, do that many members really have an interest in all new posts in every topic they have read permission for?
I guess it could be a “Hey! We’re an active forum!” thing but it really doesn’t seem that useful to me. Not as long as I can already get Notifications, New and Unread for what I am interested in anyway.