Thanks for the suggestion Tom! We'd love to hear from the rest of the community if they feel like this would be worthwhile and what the use cases might be. For the time being you can achieve the same end result via search.
I'm in favor! One disadvantage of using the search tool is that you still can't search by number of replies, which is entirely different from unanswered questions. Peoples questions could have been answered, but not marked as such, or there could be several potential solutions, none of which is "correct". But if I could sort by number of responses, I can more easily find the posts that no one has attempted to answer or no one is working on a solution for the poster. Make sense?
The search page actually has a lot of what is being requested for here. I have made a video showing some of the filtering and sorting options when you're on the search page. You'll also see that you can filter out only discussions without replies: https://www.screencast.com/t/pxOzTIljTN
I hope this helps!
Note: We will be switching to a newer and better search platform soon, but similar functionality will exist there.