Wow - some very interesting and informative responses there : thanks to all concerned for taking so much time to reply and take the conversation on.
Reflecting on the responses, it seems there is plenty to come in terms of cataloguing this body of knowledge, which sounds like a huge and worthwhile undertaking. I suppose my initial query is a less academic one: Are there generally accepted to be a smaller number of broad-brush approaches to teaching singing, upon which the myriad of contemporary (and not so contemporary) systems/approaches/brands are based upon? And if so, where would the systems and teachers who get name-checked both here and elsewhere (either in scholarly discussion of advertising - the latter being where the majority of students will come across them I'd wager) be pigeon-holed according to those overarching approaches?
I appreciate this is a blunt instrument in terms of cataloguing or starting to understand the approaches, but only if taken at face value. I suspect that for the relatively inexperienced singer a discussion that drew this information out would be both interesting and useful, by encouraging exploration of alternatives (right now I couldn't tell you which teachers or systems overlap and which are genuinely philosophically different) as well as giving insight as to whether one teacher's positive comments about another might be genuine professional admiration despite them being proponents of differing, perhaps even opposing points of view.
I hope I'm putting this across right : this comes from a genuine desire to understand some of the things which seem to underpin other discussions here and elsewhere which I think less experienced folks miss out on the relevance of.
cheers,
T