Following the discussion on "bare attention" and "sati", here are my thoughts:
I wonder if the modern teachers who have been teaching "bare attention" intended it to be a equivalent of sati or simply a preliminary instructions for students who, most often, have deep rooted habits to proliferate, to judge, to like and dislike. So explaining "bare attention" seems to be a kind of antidote to such common attitudes.
However, it is indeed true that some (or many) students seem to take that instruction to the extreme of removing necessary discriminative tendencies/faculties known as Dhamma-vicaya.
That's why teachers like U Tejaniya Sayadaw of Burma has given life to a book titled "Awareness alone is not enough" where he stretched on the importance of developing the investigation factor (Dhamma-vicaya) in the course of practice.
Last, but not least, I don't think we can really practice "sati" in its true meaning ( as in the quotes provided by Dmtro). We "practice" all kinds of things that are more or less close to it, until it actually arises, accompanied by right view .