I would expect that given fencing's linear nature, it would be more advantageous to angle the back foot more forward to push off. Why does the foot point off to the side in the basic stance?
Mainly for versatility and stability. In fencing your actions moving backwards are just as important as your actions moving forwards. A lot of people think of it as advancing on your opponent or retreating from them, but the point of those things isn't to capture or cede strip, it is to open and close distance. When you're fencing, you know your range and you know where you're most effective. When you're new, you only know these things for perfect control and balance situations. As you get better and more experienced, you also start to get a sense of where those points are during motion and in situations of imbalance. At that point, what direction you're moving matters much less than whether the space between you and your opponent is opening, closing, or static. And your opponent is trying to do the same thing. So you're both trying to manage optimum distance at the same time. Micro changes in direction and pace are really really important. If your foot is turned too far forwards, while it favors forward motion, it doesn't provide any stability in terms of quick changes of direction. If your foot is turned too far backwards, you just fall over. Posting guidelines says "Share your research" - I've been a fencer since 1985, competitive on the national level since 1990. I have taught beginners for most of that time.
It has been a while since I fenced, but my understanding of the foot position is to increase stability during a deep thrust like the one shown below. Look at the leg slightly above the "C" of the fencer on the right. Were their foot in any other position, they would not be able to extend as much.
I still remember the start of my very first fencing lesson at school. We had no swords, the instructor just paired is up and gave us a game. We had to touch each other with our right thumbs and shout whenever a touch landed. Five minutes later we were all laughing when he suddenly shouted "freeze!". We all did. "You are all standing with one arm out and one pulled back. You all have your feet at 90 degrees which means that your bodies are 45 degrees to your partner". And so we were.
The position is natural compromise that allows forward movement, reduces exposure of the body and puts the weapon up front.
In Shotokan karate, the stance is known as kokustu-dachi. It is a defensive stance that keeps the target area farther away from the opponent, yet easily shifts into a front stance/lunge (zenkustu-dachi) when an opponent leaves an opening. I assume it is the same with fencing. The back foot, at a right angle to the front (which is pointed at the opponent), provides a great deal of stability and support to a subsequent attack. As with fencing, modern karate competitors often bounce, with the back foot angled more forward. This toe-bounce gives a bit more directional flexibility, quick acceleration, and helps to keep the body loose and relaxed during a match. There is a sacrifice in power, as the acceleration from a toe bounce comes primarily from the gastrocnemius (calf) muscles first as opposed to a traditional lunge which is initiated in the biceps femoris muscle and the gluteus maximus. In fencing, I assume the overall power of strike is less important than the sheer speed of a strike. Anyway, dynamic fighting typically includes both bouncing and set feet (think of boxing, where the fighters bounce, but also set their feet for a power stroke).
We have had some considerations in our Judo training regarding the open foot-stance. I can only report here, I have no (e.g. biomechanical) informations soppurting this. It only makes sense for me.
The main points have been that:
a) The thrust forward is more stable. Having your back foot in line forces you to either rest rather on your heel, which makes it impossible to have explosive movements forward or you rest on your forefoot in order to have the possibility to accelerate forwards explosively, but having only small parts of your foot on the ground has the disadvantage that you loose great amounts of adhesion - you are more at risk of slipping.
b) Possibly not that important for fencing, but in Judo, the stability against being pushed backwards is better as well: If you have the back foot in line and rest on your heel, you tend to roll over it and you have no muscles functional to work against it (the calf is stretched), if you rest on your forefoot the point of slipping is your main problem.
Both points may be avoided by pointing the back foot to the side: Full adhesion and the possibility of explosive thrust. In Judo, another point is the mobility sidewards, but this can be ignored in fencing, of course.