I’ve always taught English as a whole language, even before I knew the term. It strikes me as utterly odd for anyone to even consider teaching a language from any other perspective. No, not “strikes”, “pummels”.
I can see, perhaps, some people becoming interested in the linguistic aspects of a language after they have become fluent, but there is no logic in beginning a language that way.
Language is communication. Language has nuances which cannot be put into a worksheet. Language is entirely social: we don’t need language if there are no other people around.
Language does not make any sense in parts. If one were to look at the process of walking, and break it down into a thousand muscle movements, and learn each of those muscle movements separately, how long would it take to learn to walk? Would you ever learn to walk effectively, especially if you suddenly had to change one of those muscle movements just because you moved to a country where they turned their foot slightly out rather than in?
If you want a language which works well in parts try mathematics.