This video shows my concern with the standard Billy Allen curb bit. Even on a well-made model, such as this Professional's Choice Bob Avila number, pulling on one rein transmits through the central joint and pushes the opposing shank forward. Does this bother the horse? Admittedly it doesn't really seem to, and many horses do well in this kind of mouthpiece, but the two cheeks should be hobbled at the bottom to prevent too wide of separation between them. I've seen the same problem in similar bits, like the Imus Comfort models and others with a joint designed to allow independent side action, yet too tight to allow freedom of movement in other planes.
(I did own a very cheap TexTan Billy Allen at one point that maxed out this effect so severely that I ended up literally trashing it. The shank opposite the one I was contacting would flip forward and then get stuck in an upside-down position, and any efforts to fix it would only further twist it out of place, making an uncomfortable situation for the horse in addition to taking all control away from the rider. The moral of this story? Buy the highest-quality tack you can afford, but still inspect its actions carefully, lest they be different from what you had anticipated.)