My kids both started in Suzuki programs. In fact, from what I can tell, Suzuki is now the leading teaching method for small kids on nearly all instruments. Teachers tend to modify the method somewhat. Since "Suzuki" is a brand, it comes with a specific repertoire. American teachers tend to draw from a larger repertoire, and also introduce reading fairly early depending on the kid's aptitude and interest.

In my observation, classical music is not a turn-off for kids, if they are young enough that they don't have a strong sense of what is "cool." Reaching teenagers is a whole nother ball o' wax, and I suspect, is rarely as successful.

Part of Suzuki's ideology involved the parents. He expected them to be enthusiastic partners in their kids learning music. This can be a problem if: 1) The parents don't like classical music. Many people viscerally dislike it. 2) They oppose all structured musical education for whatever reason, including their own childhood experience.

I grew up when Suzuki was still controversial in the US, and my training (on the cello) was along classical European lines. Music is a huge part of my life, though I now play jazz on double bass almost exclusively. I'm not sure that the less structured approach to learning guitar actually leads to less attrition. Among people I know (for instance at my workplace) who still pursue an interest in music at any level, relatively few play the electric guitar. Without supporting evidence, I wouldn't assume that the supposedly structured, old-fashioned approach to teaching music is actually less successful in the long run.

One possibility is people wait longer to quit. A student who sticks with it for 2 years might not get very far, but they pay for a lot more lessons than someone quitting after 3 months.