(I posted this feedback myself after finding out there was no formal request for it. I'm surprised, since it's been mentioned here and there. This is from my perspective as a regular user.)
not children should include all other options, yes. Including no selection is going to be something that varies in usefulness, so there's no clear answer there.
When trying to exclude trait setups representing something exceptional, we benefit from including blanks. not alignment of evil will find for me everyone who considers their alignment unremarkable (they're probably not evil), not genital amount of double also finds for me everyone with unremarkable genital amounts (probably single).
Mundane searches like not male, not female, not breast size of large are also very likely to give me good results if we include blanks.
When trying to exclude trait setups that represent something normal including blanks isn't good. not unaligned would get me everyone who's Good and Evil, which is what I want, but it'd also give me all those same people who consider their alignment unremarkable. not genital amount of single has the same problem: there's going to be a lot of singles that list. Excluding blanks is better.
There's ambiguous cases. With not game system of shadowrun I could be asking for everyone who isn't a Shadowrun character, and all the blanks fit that bill. Or I could be asking for everyone who actually has a game system, as long as it's not Shadowrun.
I think it would be wise to let people choose.
I also think some of these traits would benefit from the "unremarkable" option (like genital amount of single) being treated as a default in some manner.