I totally agree coach. I think JT wimped out on this one too. He opted to care more about Alice's conscience in the fight also rather than her desire to settle their hated rivalry. Perhaps he chose that route because in the end they are revealed as being cousins, so they had blood ties. Maybe if they did not have that relationship, he might have chosen a different ending. It was such a great build-up, he could have made a classic fight ending. I wonder if JT struggled with where to draw the line sometimes re his apparent fondness for catfights, in the sense of almost covering this up somewhat by the explanation of wanting to present strong female heroine characters. In other words, he pulled back on the throttle in some of these catfights so as to not be seen as just a outright lover of catfights.
There have been numerous instances in movies and TV shows, Westerns in particular come to mind, where a good-guy, white-hat wearing law respecting sheriff/deputy/cop takes off or puts down his badge and gun belt to fair fight a villain, sometimes with witnesses and sometimes without witnesses. That's not the hard part to work into the script. As you say, the real difficulty here is the fighting training that Alice had and could revert to during the fight. Interestingly, Marla made the comment to her husband just after the fight that she had been taking judo lessons. She possibly made that up to cover the reason for the fight, but it did make me think she was more qualified than I thought. No matter, the last thing I would have wanted to see would have been a martial arts type fight. Hell, that's not catfighting.