Earlier quoted context omitted.
As a former Latin instructor with literally decades of experience, I strongly recommend not relying solely on Ørberg. The outcomes of those who refused to supplement it with a proper grammar and dictionary were far, far behind those who used Wheelock alone. It's very popular online, but it's methodologically bunk.
Thanks for the perspective! I guess it depends on the outcomes in question If they're measured by traditional academic metrics (parsing, recalling declension tables, translating into English), then Wheelock's grammar-first approach really does optimize for that. On the other hand Ørberg optimizes more for reading fluency and intuitive comprehension, which is harder to measure on a standard Latin exam.
The fastest that I've learned a language was by buying a grammar and spending hours on end doing grammar exercises. It doesn't just work by "traditional academic metrics", it works and fast. That's because it's faster to learn something if you're explicitly shown the pattern and then you do repetition, than if you just do the repetition.