The cable chop sounds great on paper, but when it comes to the execution it's less of a core exercise and more of an arm blaster. Also, the resistance changes drastically from beginning to end.
With this method, the Swiss ball acts as a cam similar to what you'd find on a machine, giving you the feel of constant, equal tension throughout the ROM and putting that tension right where you need it.
Most trainees have the habit of waking up, shoveling down some Fruit Loops, and heading off to the gym before they've truly awakened. In other words, given the amount of prep work they've put into that particular workout, they might as well have left their Fozzie Bear jammies on and stayed in bed.