Why I am not a fan of verb paradigms for language learning

Okay, mother-tongue English speakers give me "to have" in the progressive pluperfect tense third person plural!  Now "to be" in the imperfect subjunctive second person singular!

I have been in numerous Linguistic courses, I have diagramed beaucoup English sentences and I have been learning English for 27 years, yet I have never on any occasion been asked to do the drills mentioned above for English verbs.  I have however been drilled similarly in Greek, Hebrew, Spanish and French.  Why?

This sort of drilling has been particularly disturbing to me as I learn French.  I am convinced that Linguistic analysis is good for exactly that, but not for language learning, not for language acquisition.  What I have observed this time around in the language learning process is that when I look at verbs in nice neat paradigms they are completely out of context and therefore their real meaning is lost on me.  This is a grave problem if my language learning goal is to be able to have genuine communication with real speakers of my target language.  I have also observed that those real speakers, with whom I desire to communicate, don't give any consideration to the linguistic analysis of their utterances because they are engaged in genuine communication.  They don't consider whether to employ the conditional or the subjunctive before they form a sentence, they just speak.  They don't stop in the middle of sentences to shift through verb charts, they just speak.

So, I began to ask myself, is it possible for me to get to that point of comfort with my target language?  If so, how?  Wouldn't it make sense that I should go the same route that those real speakers took?  And if I were to go a different route, could it possibly hinder me from reaching my goal of genuine communication?

What do you think?

Curious about the verb tenses I mentioned above?  I used the progressive pluperfect once in the this post, it is highlighted in bold.  I also used the imperfect subjunctive tense once and it is underlined.