I never tried that program per se, but I have trained in similar fashions. It works well for two reasons, I think. One, because it focuses on bringing up compound lifts, with the goal to add weight each time you perform a certain lift in a certain rep range ,and to up your weekly workload. Two, because it is laid out in such a way that it fosters consistency(people love to see progress, it builds confidence, and makes you love to train), and consistency will translate into progress if you train on a solid rutine.
BFS is one of those things that is a no brainer on paper. Meaning, it is gonna work for a time. How long it works will depend on how you deal with adaptation and how honest you are with yourself about your weaknesses, your willingness to bring up weaknesses, and your training IQ in terms of switching and swapping movements.