GH and Joseph:
Bias from batei din is a reality. I cannot speak to the reduction of this. But experience indicates that it is live and well, and may depend on many circumstances. What may be correct is that a broad brush assessment of this may be less than accurate. And the same BD that has a reputation for being biased towards men may adopt the opposite perspective in a specific case. I have observed this a number of times.
Hilchos Gittin is not biased at all. There are specific roles that are designated for each gender. These are not biased. The halachic discussions on the brocho of שלא עשני אשה are complex, but do not suggest that men are “better” than women. Each gender has its strengths and weakness. In the infinite Divine Wisdom, HKB”H wanted marriage between these two different species of humanity so they would together comprise a complete neshomoh. Each one without the other is incomplete. neither is better or worse. The husband that is required to give the get is not better or stronger. The wife must be agreeable to it (as per Rabbenu Gershom), and this is normative accepted halacha. Each has their own contribution to the process. That is not bias. Is a right handed person inherently biased because he cannot write or throw a baseball with his left hand?