Pretty much, yes. You are asking why would the response to this incentive affect people of different gender differently. I don’t have any clear answer to this question, other than pointing out that in the current system, we already have an existing imbalance, so there is already a difference in how incentives affect different people, and unless we determine the exact mechanism here, random changes are unlikely to change it.
By the way, this is called Campbell’s law.
https://en.wikipedia.org/wiki/Campbell%27s_law