Here's what I'd like to do:
When an issue is created, it has a field or a label or whatever that says the issue is Unestimated. We'd be able to search for all Unestimated issues this way.
When the Story Points field is edited by someone giving an estimate, the previously mentioned field/label/whatever ("unestimated") goes away.
I do not want to have my users have to worry about editing two separate fields, and switching the flag over manually when an issue gets estimated.
I also don't want to simply rely on Story Points being 0 as a way of denoting an "unestimated" issue.