Why leave read notifications in an inbox?

I am making a website with the primary purpose of creating content (specifically, arguments consisting of interlinked statements), very similar in approach to Stack Exchange. Currently, I am implementing a notification system to notify users of content they contributed to or are interested in.

At first, I thought to copy the design of Stack Exchange: the amount of unread notifications show up in an overlay on the inbox icon, and opening the inbox marks all notifications as read, yet they remain in the inbox indefinitely. However, I expect a great deal more flux in edits made to arguments: statements will be edited regularly, commented on, and moved around. The primary reason to notify users is to keep them up to date with how the argument is evolving (since they have expressed an interest in it). But, essentially, notifications might rapidly become outdated.

For unread notifications the choice is easy: at any time, remove notifications which are no longer relevant. E.g., a comment which was added and subsequently removed.

However, what to do with read notifications ('read' being similar to Stack Exchange, meaning the notification list has been opened)?

• What use cases are there to visit the history of notifications?
• Does Stack Exchange remove notification history to content which is no longer available (e.g., comments, questions, or answers)?

Given that notifications on my site could essentially be considered 'to-do' items, I am inclined to remove them when they become irrelevant, even when they have been read. Similarly, I am considering a 'dismiss' or 'remove' option which removes notifications from the list entirely. Obviously, this can easily be expanded with 'dismiss all' or 'dismiss all' for a particular argument.

• Does it make sense to encourage users to keep their inbox empty?
• Do you know of any websites/systems with a similar design/intent I could draw inspiration from?
• Any specific mechanisms how I can convey this 'optimal' (if it is) use of the inbox? As in, teach them to dismiss notifications they have 'handled'.