Although I agree that most questions a bioinformatician might want to ask could fit in one of the stackexchange sites you mentioned, I sometimes have a feeling that some site more specifically dedicated to bioinformatics issues could be useful. I know that biostars exist, and I find it a pity that this site is not integrated in the stackexchange network. I got used to the stackexchange-like interface and still haven't gotten into the habit of following what is going on on biostars or ask my questions there. Maybe it's just me not having made enough efforts yet.
Now why the already existing stackexchange sites might not be enough to host bioinformaticians' questions and answers?
The kind of question I would see fit for a bioinformatics stackexchange site would relate for instance to the use of programs or libraries specifically used in the bioinformatics field.
Why not on Stackoverflow?
Such questions might not get the attention of the typical stackoverflow user, because they deal with specific tools not used in other fields.
I'm not sure this is a valid argument, but it seems to me that questions easily get "swamped" in stackoverflow. Sometimes, an interesting programming question relevant to bioinformatics might get posted there, but go un-noticed because there are so many other questions being posted at the same time. That being said, the bioinformatics tag could help the bioinformacian potential asker or answerer.
Why not on Biology?
This community may not have a high enough concentration of people expert in the use of computational tools. It also may contain too many questions most bioinformaticians don't really care about.
Why not on Crossvalidated?
I don't have much experience with the other sites you mention, but I guess that the same phenomenon I suspect above for programming questions could exist for statistics questions. There are statistical tools or models specifically designed with biological data in mind. Questions relative to these specific tools or models might more easily attract interest on a site dedicated to bioinformatics.
These are my impressions. I'm not 100% certain yet that a bioinformatics stackexchange site is something absolutely necessary, but if it existed, I might use it.
Edit: I regularly encounter issues that I would like to ask on a bioinformatics stackexchange site. I gave some of them as examples here:
See also my comments to the present answer for examples of questions people asked on other stackexchange sites but would better fit, in my opinion, on a bioinformatics site.