This is the first time I've been exposed to systemic functional grammar (SFG) as a specific discipline or practice. But, I do think I understand the basic idea and it seems to fit in very well with the overarching trajectory of humanities studies to be ever more "descriptive" and less "proscriptive" about how to think about human phenomena such as speech and language.
So, the first question: is SFG an alternative grammar? I'm going to say no. What it actually constitutes is a different approach to grammar. It almost certainly recognizes that basic categories such as nouns, verbs, adjectives and normative expectations of word order and inflection do exist across functional boundaries, but that within functional boundaries there are additional (perhaps previously overlooked) emergent properties that (probably, likely) cohere around those functions. Think of the word "metafunction" as a "mode."
In other words, in the mode of "Hey, cutie-pie. Who dat?" there are different "rules," "errors," and other expectations that if you get serious about it, seem to constitute a different "grammar" than the mode of "Dearly Beloved, we are gathered here today to witness the union of man and wife," which in turn has its own "grammar."
I put grammar in quotes above because at this point we are actually talking about a "new" grammar, but at the same time, we really aren't. We've changed levels or modes of discourse such that it is true and not true at the same time that SFG is an "alternative grammar."
For example, it is really not possible to provide one sentence that "uses" traditional grammar and one that uses SFG grammar. The battle is not so much over what acceptable practices are, but rather how to describe them. Traditional grammar, for example, requires a lot of hard work to be able to describe certain grammatical things like "Who dat?" because it is centrally wedded to the idea that "Who is that" is the real underpinning. SFG in contrast provides an "easier," decentralized method for describing (and probably discovering new things) about grammar by being perfectly willing to cluster its expectations around individuated functions, and thus discard all the worry about such things as "how close to proper" is something like "Who dat?"
This leads us directly into the second half of your question which is about whether an overemphasis on traditional grammar limits our ability to coach people toward advanced fluency and articulateness.
The United States started to move away from overemphasis on "grammar" in the 1960's. A critical book by Mirna Shaunessey (sp?) called Errors and Expectations focused on the speech of urban students, challenging the traditional notions that their vernacular speech was "erroneous" or non-grammatical. Her work shined a bright light on the fact that restricting young students to rigid syntactical, lexical, and otherwise traditionally grammatical formulations was literally like putting handcuffs on their ability to express themselves in writing.
Among the more intelligent thinkers outside Shaunessey's urban settings, her work was easily abstracted for applicability even in "traditional," upper-middle class suburbia. Why is it that kids can almost always talk better than they can write?
To be sure, this general movement toward functionalism has been slow to reach many areas of K-12 as well as higher education. Some enclaves still explicitly resist and/or reject the the basic idea outright. The basic idea is that lessons about how to be in compliance with the formal grammatical expectations of privileged modes of speaking can be treated as a small thing and is best addressed ancillary, subsequently, or otherwise after the fact of nurturing the open expression of thoughts and an expansion of the complexity or "richness" of thought.
This is the underpinning of a statement like "parsing words into inflexible categories doesn't help people write better."
The whole enterprise challenges what it means "to write well." It's not really that traditional grammar is wrong, rather that it is very often wrongly applied to the learning process. Traditionally, English teachers distribute grades based on an absence of mistakes according to the expectations of edited, formal public discourse. Teachers working in the functional tradition provide editorial correction/guidance with regard to the mechanics of writing, but focus their grading on the accuracy, relevance, complexity, order, interrelationships, and conciseness of the ideas expressed.
This is obviously a big topic, but these are the basic ideas at stake. From what I see is, SFG represents a more comprehensive and, well, "systemic" approach to this basic idea that functionalism should trump idealism when it comes down to the usefulness and completeness of our descriptions of the "rules" (the grammar[s]) of language.