At first, I thought you were suggesting that a developed man shouldn't refrain from hitting a woman, on the basis that this exhibits a higher level of moral development. But that's not quite it, is it? Following the second level of moral development in this case will result in exactly the same action: don't hit her. (And depending on the circumstances, analysis at the third level would sometimes result in the same conclusion.)
How could we even tell, based on such an interaction? A person at the first level, or even the second level, is probably not sufficiently self-aware to say whether they're refraining from hitting a woman for a first-level or second-level basis. And they have the same outcome (no hitting back), so we can't tell by observation.
There are also external considerations to be made.
Social: I may be at a higher level of moral development but everybody has a smartphone with a camera these days. I do not want to be ostracized because I'm all over Youtube as "The guy who hit a girl" (even if it was justified). I can't just tweet "It's OK, folks, I'm at a higher level of moral development" and make it go away. Even people at higher levels of moral development can surely appreciate the benefits of having friends, and a job.
Legal: I'm probably stronger than the average woman, and regardless, the law can still be sexist in some matters. If a cop shows up and we both have equal bruises, and it turns into "he said / she said", I'm probably going to get penalized worse. (This is one reason legalized gay marriage is so important, even for straight men. The legal system can no longer simply fall back on assumptions about guilt based purely on sex. Sadly, such assumptions are still fairly common, in my experience.)
I haven't studied psychology, but I don't quite understand (this brief summary of) Kohlberg. Laws seem to me to be mostly the codification of our basest social contracts, and it's only rational to obey them (mostly) to preserve one's freedom. If I don't hit someone because I'm following the social contract, is that the highest level of moral development? Or the lowest, because this social contract is also a law? Or somewhere in the middle, because I'm looking out for myself, by not wanting to be arrested? Motivations are difficult to pick apart, and since I'm over 5 years old, I doubt I ever do anything for only one reason.
P.S., I appreciate the "wall of text". These are complex issues and it's not productive to assume we can resolve any issue in 140 characters or less.