The advantage

With all due respect, I think you are completely wrong.

If a gun picks a GF between 1 and -1, then it is covering all possible future locations of the enemy that the wave would be able to reach. And, by definition, a random gun should have an equal probability of picking each GF. So, there is the same chance that the gun will aim at 0.2 as it will -0.2, and the same for 0.8 and -0.8. The cool thing about random guns is that they cannot be dodged (assuming the random generator is truly random, but for practical purposes, Math.random() works fine), anywhere the opponent might go has exactly the same chance of being hit as any other potential location.

I think you're being thrown off by the difference between equal and better. A true random gun will always have an equal chance of hitting the enemy wherever they go. For example, if the enemy was SittingDuck, a HOT gun would have a 100% hit rate, while the hit rate of a random gun would be something like 5% (depending on distance). If the enemy always moved in straight lines (Who cares about walls?), a Linear Targeting gun would hit 100% of the time, while the random gun would still hit something like 5% of the time (depending on distance). If the enemy was Nene, HOT would have a hit rate of about 0.0%, and LT wouldn't fare much better, but the random GF gun would still have an equal chance of hitting no matter what the enemy does.