The school has several things going for it:
1. Stick time. Even if we only estimate 4 hrs/day of actual flying, with 3 guys, at 10 min flights, that's 40 flights per student over the 5 days. As an instructor at my club, we have a 1-day-a-week flight school, in the evenings. I'm lucky to get 3-4 flights per a particular student per session. So that in itself would be 10-13 weeks. Factor in weather cancellations, other commitments, etc. and one gets to needing the entire flying season...(here in the frozen north). We try to boost the times by also training during other mutually agreed on non-"official" meetups, but that tends to be hard to work out.
2. Degradation of skills with the delays. So much of it is eye-hand coordination. And that just takes repetition to build the neural pathways. Sure, one can over-practice. But also only doing it a little bit, with great separation between sessions, and it all takes even longer. Ask any musician trying to master a new piece....Using a sim can help a lot to combat this. But it still is not optimal.
3. The same points go for instructors - lord knows I can be deficient on achieving the balance between letting the student learn vs flying for him. One moment of "I think he's good enough to catch his mistake" judged wrong...and I repair the plane. Much more time on the instructor sticks for me too would make me a better instructor.
4. A granular level of course instruction. We have a pretty good syllabus we use, and a good outline of what each instructor should be doing during different stages of instruction. But the school apparently has taken a lot of time to greatly define and refine it. We'd never get our instructors to all agree on students only using a particular way to hold the TX.....for example.
5. Focus on a specific student. Having to jump between several students, at widely varying levels, sometimes separated by longer breaks in the relationship ("What were we working on two weeks ago?") also can reset the learning curve to some degree. Concentrating on just one, from first flight to solo, is just so much more efficient....

I've had rare students solo after just 2 weekly sessions. I've got others that took over 2 years (!). One, who took years finally did succeed, and remained so enthusiastic about the hobby, he became an AMA AVP(!). But most humans just don't have the dedication that he had....
Luckily, my average has been between 6 and 12 weekly sessions.

Cost, time to commit, etc. all come into play on whether or not to sign up with the school. Learning to fly can be done either way. But they've been around long enough to show that their methodology does work very well.
I played with the idea of also going "commercial" myself. But then that would turn my fun hobby into a serious job....