I generally use the filter hasaccepted:false, and think others do too.

The clickable searches include unanswered which, on puzzling, may be more useful if it were unsolved since puzzles often get some kind of answer or answers before being solved (nearest thing filterable being hasaccepted).

I also note here that it is likely that newer users are generally unaware of the textual search feature, and will see and use the clickable ones.

Do people agree that we should request this?

(I actually do: hasaccepted:false closed:false duplicate:false locked:false hasnotice:false and am sure the tab would do something similar)