Personally, I don't see any reason to have a video record of this. Are you really advocating creating a video library of all of one's challenge fights, brawls, and whatnot? Especially if they are not part of some big sanctioned event like the UFC, and instead are just the smalltime fights that you get into in your own neighborhood? if someone actually did this, I for one would question their motivations and just what kind of a sick minded person they are. It's just a little twisted to want to collect a bunch of video of yourself beating people up. Not to mention the video evidence you are creating the first time someone decides to press criminal charges against you for assault and battery. The very notion of expecting this expresses some pretty questionable morals and ethics...
I don't expect brawls in the neighborhood to count for a whole lot, and don't see much use in having videos of them. Only people trying to claim significant fighting ability for themselves would have any need of it, and not for entertainment, but rather for being able to prove their case. For instance, most professional fighters have a video record of each of their fights. THe pro fights of most major boxing, kickboxing and MMA champions are available on DVDs. The challenge matches of the Gracies are on tape. If you're going to go around saying that "hey I personally can beat X" there should be some video that corraborates that.