There's also the thing about "the best exercise plan is the one you actually follow". The direct method isn't "bunk", it's a very good method if you take into account that students don't have boundless enthusiasm and rote learning ability.

I learned English with the direct method (the teacher was an old Esperantist free to do his own thing) and German with the traditional grammar memorization way, and I wouldn't be able to write this post in German.

For all other languages, that is, naturally spoken languages, I would totally agree. You learn them by imersing yourself in the language, culture, country.

But latin is a dead language. What you describe is what it is used for. It is a grammar exercise.

Intuitive comprehension works much better for Medieval Latin, like that used in the scientific publications of the 16th/17th/18th/19th centuries, i.e. the kind of Latin that would be used by people like Newton or Gauss.

Medieval Latin is influenced by the modern European languages, so it uses a similar word order and similar methods for expressing various things.

On the other hand for Classic Latin, e.g. for works written during the late Roman Republic and early Roman Empire, a thorough knowledge of Latin grammar is absolutely essential for understanding the texts.

The order of words can be very different from what a modern European expects, and frequently you cannot understand which is the syntactic role of some word without being able to recognize precisely various grammatical markers for case, mood, time etc.

Understanding Latin grammar in isolation is more difficult than when you also know at least some things about the historical evolution of the Latin grammar and its correspondences with Ancient Greek grammar and Proto-Indo-European grammar.

For learning any language, in my opinion it is less important to use textbooks, than to start as early as possible to try to understand something that you are interested in, for example a movie spoken in the target language or a book written in it. For Latin obviously you must start by reading some books, since it is a dead language. An example of a relatively easy book is Caesar's book about the Gallic Wars. Another easy choice is the Natural History of Pliny the Elder. The simplest way is to use bilingual editions, like those of the Loeb Library, and to consult a grammar and a dictionary whenever you do not understand yet something (because in a bilingual edition you may look at the English page to get the general meaning, which can guide you, allowing to avoid too frequent interrupts for searching a dictionary, but that does not have a word-to-word correspondence with the Latin sentence that you must understand).

There is a good Latin dictionary that is online:

https://www.prima-elementa.fr/Gaffiot/Gaffiot-dico.html

but it is a Latin-French dictionary, so you must know French (or you may use Google translate or an LLM for French, which are far more reliable for translating French to English than when translating Latin to English). A dictionary provides additional essential information not normally available in automatic translations, like which vowels are long, related grammatical forms and a long list of possible meanings with examples of usage.

A large number of Latin books are online at:

https://www.thelatinlibrary.com/

Unrelated to Latin. I speak four languages, each learned in a totally different way.

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.