The reason we teach this step is because we want you to have the sense of falling into something, of suspension and then release. For milonga, this release is a release that has some substance. However, it's also not something one would typically do in milonga (David would, but that's a different thing). The reason why is because, in milonga, you normally step on every beat. And this one doesn't. This means that the lead to say, "don't step; hover" has to be very clear (because it's not normal).
For followers: The hover-lean in the upper body is an opportunity to add a little bit of style or attitude, to express your own opinion about what the move is like.
(From a review): La Chicana is a wonderful small tango band with an original, creative composer (Estol) and a captivating singer.