Mostly because of throw.
You are offsetting two errors (squirt and aim). You are hitting the shot thick and squirting the CB to a thinner hit. When you add throw into the mix it is a subtle variable that varies with shot angle and spin on the CB.
Throw changes with the angle of the contact with the CB. Cut Induced Throw (CIT) and Spin Induced Throw (SIT) work together in this case - both thickening the angle. And the closer to straight in the shot, the more SIT affects it. While CIT throw is more complicated it maxes out at a shot angle of 33.7 degrees.
So in essence, if you hit a straight in shot at medium speed, the deflection kicks the CB ball left (for example) which, on its own would cause the CB to miss right, but the combined effects CIT and SIT throw the OB so it goes in the pocket. CIT is 0 for a straight in shot and SIT is maximum. Given the right conditions that can be 5 degrees of throw.
As the angle of the shot increases, the CIT effect increases and the SIT effect decreases. If the speed is correct they will offset the deflection from applying the English.
There is a sweet spot of cut angles that this will work. As you noted, probably from straight in up to around 30 degrees.
Speed, both spin speed and shot speed both affect throw as well. If you use this method when shooting inordinately slowly or hard, you will likely miss when you aren't expecting it.
I think there are subconscious adjustments that you make as well. Such as varying speed to increase or decrease throw and adjusting how parallel to the shot line your cue is to adjust squirt.