There are a couple of big errors in your reasoning:
1. You're attacking the top of the range. If you want to reason effectively, you can't give the side you agree with an advantage by picking the easiest opposing argument to knock down. You should be considering the bottom end of the estimate range.
2. You fail to account for Amdahl's law and assume that an X% improvement for one factor will lead to an X% improvement overall. In fact, this will only apply to skilled¹ labor wages of employees directly working for you. Yes, there are industries like advertising and software development where that is a huge chunk of total expenses, but they don't tend to be ones where wages are tightly calibrated.
3. You assume that the gender gap would have to be homogeneous. It is possible that in situations where skilled labor is a big enough chunk of expenses (see #2) to make this a strong strategy, the gender gap is much smaller.
4. Most people do not think they are sexist. They believe that they can look at resumes and evenly weigh different applicants without letting gender color their perceptions. Most of those people are wrong. But if you truly believe this about yourself, then the "hire only women" strategy is less optimal than the "hire the best candidates for the money" strategy. If you do think you are sexist, you can probably come up with a better strategy to counteract your bias than hiring only women.
4. You assume that markets are efficient. There are a number of practical factors getting in the way of this strategy being implemented. Take the intersection of people who believe there is a large enough gender gap to make this work and people who believe that they are too sexist to weigh applicants fairly. Intersect that with people who can't research effective ways to counteract gender bias. Intersect that with people who wouldn't have a problem exploiting the gender gap. Intersect that with people with the savvy necessary to start a successful business (I think we may be down to about twelve people). Intersect that with people with expertise in an industry where the strategy will work. Now take that tiny set of people and filter out the ones who just get unlucky. The remainder still have to manage to maintain the policy once the company grows to the point that they don't have total control over it.
¹ Unskilled labor gets outsourced, and in the Chinese manufacturing industry, the gender gap is exploited heavily.
1. You're attacking the top of the range. If you want to reason effectively, you can't give the side you agree with an advantage by picking the easiest opposing argument to knock down. You should be considering the bottom end of the estimate range.
2. You fail to account for Amdahl's law and assume that an X% improvement for one factor will lead to an X% improvement overall. In fact, this will only apply to skilled¹ labor wages of employees directly working for you. Yes, there are industries like advertising and software development where that is a huge chunk of total expenses, but they don't tend to be ones where wages are tightly calibrated.
3. You assume that the gender gap would have to be homogeneous. It is possible that in situations where skilled labor is a big enough chunk of expenses (see #2) to make this a strong strategy, the gender gap is much smaller.
4. Most people do not think they are sexist. They believe that they can look at resumes and evenly weigh different applicants without letting gender color their perceptions. Most of those people are wrong. But if you truly believe this about yourself, then the "hire only women" strategy is less optimal than the "hire the best candidates for the money" strategy. If you do think you are sexist, you can probably come up with a better strategy to counteract your bias than hiring only women.
4. You assume that markets are efficient. There are a number of practical factors getting in the way of this strategy being implemented. Take the intersection of people who believe there is a large enough gender gap to make this work and people who believe that they are too sexist to weigh applicants fairly. Intersect that with people who can't research effective ways to counteract gender bias. Intersect that with people who wouldn't have a problem exploiting the gender gap. Intersect that with people with the savvy necessary to start a successful business (I think we may be down to about twelve people). Intersect that with people with expertise in an industry where the strategy will work. Now take that tiny set of people and filter out the ones who just get unlucky. The remainder still have to manage to maintain the policy once the company grows to the point that they don't have total control over it.
¹ Unskilled labor gets outsourced, and in the Chinese manufacturing industry, the gender gap is exploited heavily.