"It's one of the most pervasive problems in tech: ingrained sexism that sees women looked over for promotion or often not given a job in the first place."
Where is the evidence of this? There are relatively few women in technology but the main reason is because there are relatively few women who want to be, who study the right subjects and apply for technology jobs. I have been recruiting for developers, with a bias towards dual skilled people with SW and Physics, Elctronics, Biomedical engineering for 30 years and the number of women who have applied in that time is a tiny percentage perhaps one in fifty. Any women who applies automatically stands out and that alone is a big advanatge let alone a desire to balanced teams. The problem is that the number who are any good is no better than for the men so the handful who apply are then whittled down by the handful who are actually competent.
Why do we endlessly worry about the proportion of women in tech, have lots of schemes to encourage women and yet pay no attention at all to areas where women dominate? If we look at current enrollment on degree courses the big issue is the lack of boys yet nothing is done to address this, in fact the opposite, everything is done to increase the imbalance.