The quality of Labor does matter.
The quality determines the pay and level of incentives.
On the example of the military; If a woman has an inherent disadvantage in combat, then she'll perform at a lower level, have harder time going up in ranks, and, eventually, be discouraged from continuing and potentially discourage other women from joining.
That's how the polarization happens in the market.
"Average" is an old, family norm.
"Individually" goes against what you just claimed.
It's a statistical term.
As an example;
The risk for women to develop breast cancer is around a tenth of one percent.
Meaning that, on average, women will not develop breast cancer. However, occasionally, individual women will break the rule, due to a number of genetic and environmental factors, and develop breast cancer.
See, those two terms can work together.
There's no point of taking this as "average" since that "average" were norms created by elites to defend patriarchy.
The average is a term we use to describe the mean of a set of items or data in general. It's not a 'thing' in and of itself.
Furthermore; Define your premise.
For the wage gap stuff;
The wage gap is based on taking the sum of earnings for all women and all men in a country and comparing the end value.
If we were to take into account geographic factors, fields, experience, position, type and size of company, type of contract, and tasks, then did the comparison on an hourly basis rather than an annual one, then, in most developed countries, the wage gap between genders doesn't exist.
Only felt I should mention it since you just hinted at the amount of work, which usually comes right before mentioning the wage gap. So, put it out there pre-emptively.