Well, my thoughts on this come from the perspective of growing up in a single parent household, where there weren't parents fighting at all...
Add in having read a lot of stuff by John Gottman and his love lab research.
Reading actual studies on habits of couples who are happy and who are not, I don't worry so much about "fighting fair" in front of the kids. Because, honestly, fighting fair is not the panacea it is cracked up to be, by studies of actual couples. Learning how to fight fair will not save your marriage, and won't teach conflict resolution... because sometimes what we are disagreeing about isn't going to be something that we can compromise on, or sway people on... In his love lab experiments, he has several examples of couples disobeying the fighting fair rules constantly who still remain happily married (and rate themselves as happy, and by researchers accounts demonstrate their happiness)HOWEVER, "healthy" people in healthy relationships accept the bones that their partner throws them (in general), and do not have contempt for their partners (contempt is the big sign that a marriage is going to fail).
So, when someone is very angry and says - "I still love you, you jerk," the partner doesn't turn around and yell back, "well you have a terrible way of showing it, you asshat," with a level of vehemence that carries the fight forward... Instead, the comment might elicit a fleeting smile with the same spoken reply - with a much more ironic flair... with an "I love you, too" added in. Heck, it might even end the fight.
Honestly, the ability to make repair attempts and the ability to accept them when they come from your partner in the heat of anger is probably one of the best indicators that a marriage will continue. A key thing that I have learned (that was never modelled to me, because I had a single parent), is that some fights (in fact often many fights) never get resolved. They cycle over and over and over. The couples who are able to deal with this (usually via repair attempts) are the ones who stay together. I do think that the rules of fair fighting are important, but I also think that they should play second fiddle to teaching children to acknowledge when your partner is trying to back out of a fight, or to repair things, or whatever - even if the fight is not resolved.
I think back to a couple I knew who eventually got divorced. They went to counselling and were taught the rules of warfare. Thing is, he already did most of them, and she did not. Suddenly all their marital issues were the fault of her lacking self control. She was to blame. It didn't matter the issue that began the fight, her not fighting fair became the scapegoat, and provided an issue that he could feel contempt for her on.
Dh and I, on the other hand, went for counselling and our therapist gave us a bunch of studies from John Gottman and his love lab. We were taught how to make repair attempts, and why it is important to acknowledge them... Well, we don't always fight fair. We try. Many, many times we succeed, however, the biggest thing for us that keeps us okay is learning that it is okay to disagree, that some things aren't going to be solved by arguing - learning how to fight fair seems more to focus on disagreeing and fighting... whereas learning repair attempts, ("hips" for those familiar), and engaging more in these, rather than in "pips" (negative, needling interactions often laced with contempt) seems to focus more on resolution. Resolution apart from actually fixing the problem - end the fight, not necessarily the problem. Some problems can be fixed. Some will never be.
Anyway, I am not against fair fighting. I just think that it isn't the first priority in a healthy relationship.
Regarding fighting in front of the kids. I think that they key is that they always know that mom and dad love and respect one another. Even if, over something that completely polarizes them, they sometimes act like assholes. Other studies have shown that kids need resolution to feel safe that fighting in front of kids (caveat: in a healthy relationship) is BETTER than fighting away from them. Fair fighting, which may leave fights completely unresolved, doesn't help kids - instead, adults actively engaging - mid fight - in reconciliation even without resolution is what helps kids. Kids are aware of heightening tension and allowing them to see the process of disagreement to reconciliation is important in helping them feel safe.
The other thing to consider is that couples who have made a pact to not fight in front of the kids often find themselves BEGINNING a fight in front of the kids, move the fight out of range of the kids - so the kids only see the beginning of the fight. They are still worked up over the stress of what they saw, they don't wind up seeing the resolution, so they wind up at higher risk of anxiety issues (Nurtureshock is really a great read.).
However, my perspective is probably different than most people, because I went into marriage thinking that every problem could be solved and should be solved, and that if you just discussed things the "right" way (aka, through fair fighting), wedded bliss was truly two people with one mindset. Boy was that an unhelpful attitude... I blame the 90s psychobable...
I have since discovered that there is no convincing my husband of some things, just as there is no way that I am going to be agreeing to everything he says and does. And that is perfectly fine. Sometimes we even hash it out, and realize, yet again, that on certain issues, we are simply wasting goodwill. That was more important a lesson for me than fighting fair.