Saying "women are worse at negotiating" is really not the whole story. Women are less likely to negotiate, and less likely to negotiate in ways that are most effective for men, but it's not because women are bad at negotiating, but rather that women are punished for attempting to negotiate. A woman who attempts to use the same negotiation strategies that are effective for men is likely to be considered abrasive, hostile, "not a team player", etc. and is more likely to be passed over for promotion, to be given an even smaller salary / raise, or to be dismissed altogether.
Women's approach to negotiating is effective and rational given the constraints, even though from the outside it may seem like women are bad at negotiating.
Evidence is that as more women enter a field, or start gaining visibility, salaries typically go down. This is why people assume "women choose lower paying roles" - the reality is that people see any jobs that women do as less valuable and compensation over time adjusts to meet that belief.
Women's approach to negotiating is effective and rational given the constraints, even though from the outside it may seem like women are bad at negotiating.