I really tried but ultimately found it frustrating - I think I honestly do learn best with a good amount of structured tables, going through grammar etc. Certainly that's how I've been learning Hindi (via Wiktionary & Snell, supplementing Duolingo) in which I've progressed far beyond where I ever got to with Latin via LLI.

Just hit too many blocks where I sort of have the understanding of what it must mean, but I want to ask someone 'why is it inflected in this way here but different there?', and of course there's no explanation of that. (By design, I just don't like it.)

Perhaps my ideal would be something like LLI but interspersed with grammar-oriented explanation between chapters.

It's just not a grammar book, it's a language book in the sense that it teaches how the language is used rather than "constructed".

I always recommend people learn the use of a language before the grammar at the beginning, and then transition into much more intensive grammar study later, likely exactly at the point when you got frustrated is when introducing grammar would be perfect. This is especially true when the written grammar of a language can look very different than the sound of a language (especially if written differences are hidden by identical sounds in the language, like in French).

Yes exactly, but I think the trouble is that it's too popular to say 'people learn by immersion, not by grammar and tables, immersion is how we learnt our first language after all'; when actually, some people do prefer (or at least benefit from additionally) such rigid grammarian teaching.

I've learnt so much more from studying conjugation/declension tables on Wiktionary than I have from trying to converse with fluent/native speakers, who can't explain to me why or tell me how to spell it (sounding/typing it in the English alphabet).

Is it even possible to learn exclusively by immersion as an adult? I was under the impression that roughly around puberty, we lose a good part of our ability to just pick up languages and a combination of study and experimentation was required afterwards.

Is this a sensible approach to learning any language from a book? Or does it only make sense with a "dead" language that we mostly know from literature and inscriptions?

It does make more sense with Latin, because while Latin has always been and still is spoken, much of the value of the language comes from its literature (of which 90% has never been translated).

BUT, the natural method plays well with extensive reading/comprehensible input, where you just read a lot at a simple, pleasurable level, allowing it to ramp up gradually.

This is how I learned much of English as a native speaker, after all!

So I intend to use this approach with other languages in the future as well.