Rockdog, seeing only the point when you fired your guns would be mostly useless. You need the parts leading immediately up to it, as well, otherwise you can't tell if a plane suddenly accelerated or decelerated right before you fired, or if he jinked, any number of things can "throw off" your shot, and without a better picture of the fight, it's not helpful JUST to have the footage when your guns fire. If all you want is picturesque footage of planes blowing up, fine, but for the learning purposes you state it's far better to record the sortie, watch the film, and delete it afterwards.
Note you can always stop the film after a fight, and then just skip to the last 3 minutes of any film you review when you want to see your gunnery. One of my squaddies does that.
Doing this, looking at films to find your distance to a target, is a good way of setting your convergence, but it's not very helpful (by itself) for figuring out anything else about how you won/lost the fight.
On top of that, you can't roll the film BEFORE you press the trigger. It can't know when you're going to and then start 15 seconds early. It has to be already running. That's the price you pay. Luckily, running film requires little to no system resources, and takes up a lot less space than actual video footage. When I run FRAPS in a game it's a massive file even for short durations. A 5 minute half-screen recording can be upwards of 3GB (yes, GB) in size, whereas a 2-hour scenario frame in all its glory will clock in at 17MB or less.