Rope halters - with the "extra" knots or without - are a WONDER for training. The horse can't lean on a rope halter like they can a regular nylon/web halter. This requires the horse to give to the halter much faster, whereas in a nylon halter they have the wide straps they can lean against. You can easily see the difference in the horse's understanding if you switch from a nylon to a rope halter.
The extra knots simply quicken the understanding even more. Same thing in that you don't need a rope halter to train, a nylon halter works - but a rope halter makes the process easier on the horse. And you don't need the two extra knots, but having them makes the process even easier and simpler.
And like tinyliny said, if you get one that is too limp and soft, they're just a pain. That's another reason I like CA's halters - the stiff rope they are made of. I'm sure you can find cheaper halters with just as stiff of a rope - just like the cheaper double knotted halters mentioned above - but there is absolutely no selection of anything in tack shops around here, so everything I buy is off the internet where I cannot feel the item beforehand.
every ride counts.