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.