I'm pretty sure that Hal has never claimed that it is a game of 3 angles. I think that he uses the 3 angles because there are easy to understand reference points for them in terms of ball alignment for particular shots. It has always been said that Hal has different systems for different situations. If this system breaks down on cuts of more than 75 degrees, he'll probably tell you how to recognize that, and then give you a system to help.
I'm also going to go way out on a limb and guess that most of the stuff that has been posted by (or attributed to Hal) with respect to angles on a pool table has been to get people recognize the angles. Knowing that a half-ball hit gives you a 30 degree cut doesn't help if you can't recognize what 30 degrees looks like on the table.
So, you look at a line from a ball to the pocket. Intersect that with the line from CB to OB. Approximate the angle, and it gives you a starting ball fraction to work from. Pockets are 2x wider than a ball, so it gives you some fudge factor immediately. After that, I don't know how he advocates adjusting to an intermediate angle. BHE is one possibility (not with a Predator, tho

). Maybe 35 degrees is 1/2 ball plus 1 tip of BHE.
Anyway, that's just wild-ass guessing. But the point is that nobody, including Hal, really believes that 3 angles make all shots. But 3 convenient, easy references may help people who have difficulty aiming to start with.