Most email clients using a "POP3" connection have an option to
    "delete email from the server after N days".
 
So when there is a mailbox that no human actively maintains, you can
    continued to forward to whatever personal emails are convenient for each person, but
    somewhere configure ONE email client that connects to all the email accounts and
       deletes the email from the server after 30 days
 
This way
    The email server has a persistent copy for 30 days
    Your email client has a persistent copy for all time
    And mail boxes do not fill up.