And that problem somehow goes away if you store that same information in a separate system?
A ticket-system like JIRA is the same as an e-mailclient to me. You sort by activity, having the most active tickets on top. You can flag/mark them, you can put them in different boxes or just use tags,... All are just means to create order in chaos.
But I would never think to move my old e-mail to a different 'system' than my normal e-mail(client). I never think of old e-mails or drafts as something I need to clean up.