As we all know, tango allows far more latitude and more readily accommodates dancing to the piano, the bandoneon, the violins, or, my favorite, to the vocalist. In particular, many of the tango singers are not simply vocal versions of d'Arienzo's driving beat. They float across measures, even in d'Arienzo's Orquesta. They start and stop at times which are not where one might step if dancing strictly to the compas. A very interesting exercise that I do sometimes is, when the vocalist is singing, step only on the last syllable of the last word of the vocal phrases. I'll pick, say, Cambalache for this. Then Canzonetta, and then Remembranzes. Etc. I also play other similar games, dancing so that I adhere to the feel and phrasing of the vocalist, ignoring (sort of) the rest of the orquesta.
For me, this creates a very different feel that just stepping in the compas. This is what I was trying to get at earlier. Not that the music wasn't important, but rather that it is so much more important than just the rhythm. Although the music is (usually) recorded, I try, not always with success, to dance as though I am having a conversation with both my partner and the orquesta.
I might change this to, "As some of us know" (like you and I). Not everyone knows what you are describing. Some strictly dance to the beat, and there's nothing wrong with that.
Others, like you (and occasionally myself), will also take our "cues" from the lead at times. It's a very personal thing, IMO. A lot of the time, what I'll do is step on the beat, but change the expression of the step, based on how the emotion of the song moves me, (assuming I'm not spending most of my thinking about how to avoid the guy taking multiple steps backwards into me).
Long ago I rejected all the liquid/dynamic embrace stuff
and began to seek the dance in tango. And simply put it's
a partner dance to tango music. What you make of it is up to you,
what you think a partner dance is is also up to you. I've already
expressed what I think a partner dance is, and that in tango
the connections are not only the physical and the sensual
but also aurally rhythmic as in most if not all partner dancing.
Of course what you do with the rhythm once you are experienced
is up to you but it still remains the underpinning and first you have
to know and feel your partner. Don't leave her behind.
I could at this point write a dismissal of your assessment of the
Tango and Chaos videos you referred to but I actually feel that
Rick McGarrey was mistaken to analyse in the way he did.
They merely demonstrate quite clearly that the men use their feet
as needed for the movement which results in the quick double step
foot change: it's practical not musical.
Modern dance is a sort of modern equivalent but about form
and bodily expression and rhythm is often not much part of it.
My ex-wife was a modern dancer, she had no clue about
what was necessary for partner dancing. We never danced.
I know contemporary (modern) dancer who practice partner dancing.
Non-verbal communication is excellent with her.
When dancing with her it feel much better than looking.
Only when going extreme she lose it because of bad technique.
Watching her dance is an eye-sore. But it's very enjoyable to dance with her.
Are you supposed to always keep a slight bend in both knees while standing? Is it one of those things where they tell you that you want to eliminate the bobbing but it's more of a "keep in the back of your mind as a feeling" rather than something you ACTUALLY do?