I believe this way of training is ideal for the genetically typical guy with a life outside of the gym. Let me tell you some of the reason I like this way of training:
I've been lifting weights three times a week for over twentyyears now. Training three times a week has served me quite well. Yes, I've met guys who train more often than that. But I've met relatively few that trained five or six days a week for a lifetime. I believe most us just won't consistently have 5-6 days to train over the course of our lives--not unless you are a professional athlete or bodybuilder.
There's also the issue of allowing your body to adequately recover before you train again. Advanced trainees, for example, may find it difficult to do squats and deadlift every week--the lower back can take quite a pounding if you don't give it time to recover.
I've also found scheduling my workouts are much easier if I only have to train three days a week. I love to train, but my life doesn't revolve around the gym.
Let's say, for example, I have to skip a workout for some reason. I've found it's much easier to make up for that "lost" workout if I have fewer training days to fit in. Trying to to this on a 5-6 day split is really difficult.
I think beginners should do full body workouts at least six months. This may be different from what you read in bodybuilding mags, but remember--we are talking about the "average" guy. Programs like Muscle Gaining Secrets take this old-school approach.
Fewer training days allows you to do this kind of training and gain that first 20 lb of muscle. The best strategy to gain weight is to train enough to stimulate growth, rest, and repeat.
More advanced lifters will benefit from a basic, upper/lower body split. It would look something like this:
I train like this using programs from Minimalist Training, and I've found it to be very effective.
One final 3-day split program I should mention is Triple Threat Muscle (also by Jason Ferruggia). This one is designed for those who want to train more like athletes and develop a lean, muscular physique (vs a bulk bodybuilding physique).