I learned more teaching than I ever did in school and I still have a long ways to go.
While I am sure this is true, it's not relevant. If it were, you could go straight to the left seat from being a CFI, and it would be a required rating.
Everywhere else in the world the airlines take folks off the streets and spend the money to develop them into an airline pilot - to name a few: Cathay Pacific, Singapore, EasyJet (great article about this/them in the current issue of Airliner World). A JAR costs a buttload, but it's paid for by the airlines. In fact, I'd challenge that at least 30% of the folks in flight training in the US are on one of these programs, as the CFI & rental rates are way cheaper in the US even when you include lodging. Almost all the ones going beyond a PPL at the local school our here in Oxnard are. Without that system here, CFI is an efficient way to build hours, but I'm not sure how teaching stalls in a 172 equates to avoiding the jetstream so the passengers don't spill their drinks or diverting for a medical emergency.
Also, most military pilot's don't do an instructor tour, or even have a CFI ticket, but get readily hired. They've proven to be trainable, adaptable and able to execute standardized operations.
What I'm saying, is that while you may be a better
pilot, CFI experience will not necessarily make you a better
airline pilot. I'd say if that is your goal, get there the fastest way you can afford. ATP et. al. are going to teach you what the airlines want you to know (otherwise their program would fail) and the rest you'll learn while during your 2000+ FO hrs on your way to Captain.