How important is seeing the face of the instructor?
I cannot cite studies, but extensive anecdotal observation (maybe 5,000 undergrad students, 500 grad students) suggests that about 1/4 of students do not need, or do not care, about the person who is the instructor. But a vast majority, perhaps 3/4, do care. There is a sense of needing/wanting reassurance from a person, and caring about the insights of a person. The lack of this need/want comes in (at least) two very opposite forms: obviously the oblivious/incompetent failure to see what's going on, but also the relatively-very-competent student who scarcely needs or wants reassurance and has better ways to spend their time. The middle ground seems not to exist.

So, operationally, for almost all purposes, the person who is the teacher matters, whether or not they are a truly wonderful teacher (as long as they're not completely inert as a human being). 

(The "funny case" is the few students, both at undergrad and graduate levels, who for some reason expect/demand the teacher to be an automaton, reciting a text, not looking at students, not caring about students, not contributing, not critiquing, not improving. Yet they come to class rather than read the book? Maybe in anticipation of "books on tape", to have the classic text read to them out loud, in a room with other people?)

(The aspect of trusting in the expertise of the instructor seems, sadly, less relevant than the mandated understanding of their "authority". Tsk.)