However it seems these teaching methods are ineffective as most of the dancers just look the same no matter what they're dancing to, and can't clearly mark phrasing.
To be fair, the formative years in tango for a beginner, especially a leader, can literally stretch to a decade or more, depending on one's motivation, starting point, access to role models/actually good teachers, et cetera...
And it's made worse because most people on average don't really have much interest in going beyond hitting the beats right; there's definitely a lot more people that are way more interested in other things, like the embrace, or interesting movements.
And, I think, training musicality is not a trivial task at all, and there aren't that many teachers who are both willing and able to teach that — pair that with how one needs to put in sustained effort over a long period of time for (perceived) smaller gains relative to what one gains from classes/privates in one movement or another... Yeah, not looking that good.
It's easier to build muscle memory for most tango movements than to train one's hearing, listening and expand one's musical sensitivity to more than just the surface. I don't think non-basic music theory is strictly necessary for tango musicality, but even the basics are a stumbling block for people too.
This is the part where I'm a bit conflicted, because while I don't consciously register modulation or changes in tempo or tone colour, I have all that information stored in my subconscious already, so I can feel all of it. And that's where my problem lies, because "feeling" music might work well, but only up to some point, and is generally limited by one's innate and learned ability and knowledge.
It may very well be the case that that's enough for people, but then it's also the cause for a lot of problems in musicality classes/getting less than positive feedback about musicality. Over the years, I've encountered plenty of people who balk about
consciously thinking about music, despite wanting to improve musicality for one reason or another.