The people in control of Greek teaching.
No one is in "control", nor is there a conspiracy. Nor is there anything particularly monolithic about how Classicists teach. I've taught the same courses rather differently from some of my companions, and I'm sure if you talk in terms of nations (and continents) the divergences become even more notable - within certain parameters.
are the product of a very out dated and ineffective teaching system. Those who make it through such a filter are those for whom learning Greek was second nature and hence don't realize why there is anything wrong with current teaching methods. .
You would know that how? I'll answer since I came from a non Classical background and entered the academic system, I don't think I passed through any filters. There's nothing outdated about teaching methodologies and many places do indeed keep up with what second language acquisition research suggests. But we're not talking about a natural spoken language, however much people would like to say otherwise.
The methods we do use are tried and tested, not ossified and antiquated. I think I should re-iterate what we do, do. We need to teach students to read Latin and Greek with rapid fluency on one hand, but able to sensitively recognise not only style but register, dialectical differences and so on as they read. In turn, they need to be able to go beyond the OCT/Tuebner, so they need to know the language well enough to pass into Papyrology, Textual Criticism, Palaeography and so on at the very least. Most places want their students able to explain morphological forms, categorise syntax, understand phonology and so Philology is often a requirement.
This is the base line and the current methodology is the only one that allows these skills to be passed on, especially within time constraints. Moreover it's a good method, I'm pretty sure I can read Hittite faster than most people can read Greek having messed about with all this modern fluff. If a better method comes along, I'm pretty sure everyone will want to adopt it. Not least because the current one is a massive sink in terms of cash and effort, which is probably why so many universities aren't producing capable students.
Given that I have more faith in the ability of an enthusiastic amateur who is open to trying things out to see what works with this particular child than most of the current experts.
I fully believe in the power of the amateur too, I also think its important to draw a line between why people are learning these languages, sure, and someone should produce better learning materials for those who don't have to pick up the above skills. Lingua Latina is a perfect example of something which opens the door to Latin literature, but you could read these books a dozen times and still not understand what's so weird about the word bos.
Nor can I speak for the experts, though hopefully if Textkit 2.0 is around in 15 years I'd hope I'd be able to then, but I think most of them would at least raise an eyebrow. Michel De Montaigne had the best shot at this: his servants, teachers and father spoke to him in Latin; by the time he was an adult he forgot how to speak most of it anyway.