Notes towards a pedagogical grammar
"The combination of the simple present tense with action processes expresses what are often called habitual or timeless actions -i.e. actions which are repeated regularly over a period of time including now."
Graham Lock: 'A Functional English Grammar'
"The esential characteristic of the present simple is that it expresses the speaker's view of the event as a timeless fact. Paradoxically, not only is the present simple not about present time, but it is not about time at all."
Michael Lewis: 'The English Verb'
"How shall I answer the question whether Euclidean Geometry is true? It has no sense!... Euclidean Geometry is, and will remain, the most convenient".
A grammatical explanation is neither true nor false. It is only more or less convenient. Teaching been as an irregular participle of go might appal grammarians, but it helps the student towards easy utterance of sentences such as I have been there before.
A pedagogical grammar would only include explanations of language that helped the learner towards more accurate and fluent production. This would necessarily involve much simplification, and perhaps the jettisoning of many categories (and jargon) considered essential to the prescriptivist and descriptivist alike: adverbial/prepositional distinctions, tense/aspect distinctions, predicate/complement distinctions.
These distinctions might more usefully be replaced with a series of disparate spectra describing the underlying pragmatic values and meanings of certain grammatical contrasts: general-specific; past-non-past; functional-descriptive; real-unreal.
The overall aim would be to avoid creating a comprehensive, regularised structure. A pedagogical grammar must not become a separate, secondary structure that requires study, but must be a toolkit to help the user build the primary structure, that of the language itself.