Michelle Goldberg has written an excellent article about the dreams and nightmares of those who would like to see one half of humanity a little bit more often represented in positions of power. Of course, to even address this question is for some a clear sign of identity politics. What's not identity politics is to always have men leading countries, and in the US, with one exception, white men. That last sentence is for clarification, in case you are unclear about what non-identity politics might be.
You should read Goldberg's article, because it is nuanced and also gives the results from many studies which suggest that being female is a negative for politicians. What I wish to discuss is one quote from the article, by the researcher Dan Cassino who has studied the role of sexism in not voting for women politicians:
According to Cassino, the long-term solution to male anxiety about female leadership “is that you run women so often that it becomes absolutely unremarkable.” Seen that way, the next primary could mark the beginning of this process. “It’s a coming of age,” Lake says. “It’s not just about a woman candidate. It’s that all the best candidates are women.”
This reminds me of early work by Virginia Valian (or at least reported by her) in her book Why So Slow. She describes studies where the study participants were asked to rate various job applicants for a job in a firm. Both the applicants and the firm were fictitious, but the participants were told what percentage of the firm's labor force already was female, and they also knew the sex of the various applicants they were asked to rate.
The results of those studies tell us that if the number of women the fictitious firm was already assumed to be employing equaled or exceeded some critical mass (possibly 30%), then female applicants were judged as just people with particular job skills. If, on the other hand, the fictitious firm was supposed to employ fewer women than the critical mass, the female applicants were judged as representatives of "womanhood" first, and that judging was likely to elicit all the stereotypes the participants, both female and male, had about women.
If the same results apply to politics*, then what Cassino suggests could be true, and also a detour around the road blocks the sexists have erected on the basis of Hillary Clinton's candidacy.
It's her almost unique situation as a very powerful political woman in this country that makes assessing the role of sexism in her treatment so difficult. A sample of size one lends itself to few clear conclusions, though I'm pretty sure that Hillary Clinton has been scrutinized through a magnifying glass while one Donald Trump has been allowed to get away with anything, and that suggests to me that Clinton's sex had a role to play.
Clearly, then, we need many more women to enter politics. That sounds awkward, given the treatment they might expect, but if the critical mass could be achieved the sexist treatment would fade away or at least look for other interesting targets for attack. On the online, say.
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* I see something of this sort happening when newspapers etc. report on the filling of important posts. If the job goes to a woman the article rarely even addresses that, with the exception of jobs where the appointed woman is the first female job-holder ever. What the comments to the articles say is naturally a horse of a very different color. But nothing good comes from reading unmoderated comments.