Perhaps there are some factors that would lead to unequal outcomes that would not be corrected, but I expect that these, including the ones you describe, would have significantly smaller effects than what we currently have. And I expect that those would have been the initial impetus causing a runaway feedback effect which would cause what we have.

So, really we have two functions. One function produces the number of men and women applying for the jobs. The second function produces the number of men and women occupying the jobs. The second function is the one we've discussed wanting to control to be either fair or unfair. And yes, with inequal inputs, a fair function produces inequal outputs.

The first function, we are assuming for now is beyond our control, and the inputs to it are largely unknown and/or beyond our direct control. It is a product of experiences, societal norms, encouragement, discouragement, and personal interests. The first function directly generates the inputs to the second function. As I understand it, you are postulating that this first function is inherently inequal to the point of generating the current applicant proportions we are seeing, and that the output of this function is not significantly impacted by any inputs that are the output of the second function (feedback effect). I would argue that the first function, while possibly inequal, is not sufficiently so to create what we observe, and instead, is reasonably impacted by the output of the second function. Thus, the feedback effect.

Anecdotes I've read and witnessed seem to indicate that there are factors that reduce the number of females who make it to the application stage that would not exist if females were not already a minority in the workforce. Males in an all-male team do frequently develop habits that would put off most women who join that team as a newcomer. This doesn't have to be intentionally malicious to discourage a woman from continuing to work in the field. If women are made to feel uncomfortable, intentionally or otherwise, they are less likely to stay and to encourage other women to join, and more likely to actively discourage more women to join. And it seems very likely that a 50% female workforce would go a long way to removing uncomfortable work environments. And this can happen similarly at the college level before ever getting to real work environments, with women facing friction in mostly male programs.

Then there's the conception that it is a typically male job, just because there are many more man than women currently in it. This isn't malicious either, necessarily, it's just the way human minds work. You see mostly men doing something, you associate it with men. So you get a stronger unconscious gender affinity just because that's the way it is and has been. And that affinity leads fewer women to try the field out, fewer people to encourage them to try it out, and more people to encourage them toward other fields or even some people actively discouraging them, possibly those who have previously dropped out of the field or possibly just naive types.

I'm sure there are other examples of ways that an existing imbalance in the workforce impact the balance of those attempting to join the workforce and making it all the way to the application phase.

Also note. I'm not making any claims as to exactly how strong this feedback loop is. Just that it is strong enough to make a significant difference over a significant amount of time. That time frame may be decades, or it may be generations. I expect that at a minimum, we'd see a far greater natural equality if it were artificially enforced for 50 years or so. After that, you could have a system that is almost entirely fair, perhaps occasionally adding a small balance to restore it any time it approaches a significant tipping point again.