Of course there is some truth in all these answers... Equally, in my opinion, there is the subtext of the relationship between the correspondents, whether it is stable (if not "peer"), or whether it is yet-to-be-established, possibly peer, possibly not.
The slightly-red herring of "efficiency" is interesting, but I think fundamentally an excuse for taking slightly less care than one might, whether with up-status or down-status correspondents. Yes, if one email is among many in a flurry of back-and-forth between familiars, that's wildly different from isolated emails between strangers who have yet to establish a relationship.
The probably more statistically-relevant question could be about students emailing their instructors, and the replies. If the goal is to show respect, then use of an honorific, and investment of an extra 10 seconds to format the email, is an investment with a great return.
About more-senior students and faculty supervisors: same criterion... namely, if your goal should happen to be conveying a token of respect (as opposed to conveying familiarity), a few seconds' effort will be well repaid. (If a particular person really wants to be first-named, give them the chance to tell you that, rather than presuming, or even asking... the principle is always the same.)
If the person you're addressing is older than your parents, maybe as old or older than your grandparents, ... if nothing else you should imagine that they have had a different cultural experience. Not necessarily better or worse, but different. In particular, some decades ago, in the U.S., in my experience, youngish people would never address older people by first names, except in highly ritualized ways/settings. Some older people in fact chose "radical seeming-familiarity" in their interactions with younger people. This slightly confused me at the time, although, on one hand, it seemed sooo egalitarian. On another, as I thought about later, it is only the really, really powerful people who can afford to pretend to not be what they obviously are. Hm.
(FWIW, my 20-something daughter makes a caricature of first-naming me both in person and in email (and in text), but fairly tongue-in-cheek.)
Bottom line: take into account your recipient. They may have expectations (duh!)... which may or may not include courting "familiarity" in language. They may or may not feel that their own status allows them to be curt with you, should they feel the need... sigh...
Another summary: if the primary information in the emails is pseudo-objective, probably people will be less interested in the social information. On the other hand, if there are significant social issues being negotiated by voice, language, tone, form-of-address, etc., then ... well, gosh, yes, voice, language, tone, form-of-address will matter.
Edit: the form of responses to your emails certainly does convey something about the attitude of the responder... however, it depends (apparently!) enormously on the preferences of that person. There are at least four different cases... (1) brusque, brief, and in fact is not interested in you (2) brusque, brief, but may or may not care about you (3) polite, but does not really care about you (4) polite, and may possibly care about further interaction, but it's unclear from this preliminary communication. You cannot begin to understand the nuances of response to a "cold-call" email without knowing the person and their preferences.