I'm quite aware of the fact that the reasons for features of languages have nothing to do with planning, but I've never said or implied that that was the case.
I think I may have misunderstood where you were coming from in some of your comments. To me, the fact that a language has such a feature almost
automatically means that feature has (or once had) some purpose. Otherwise, it would never have been there. It seemed unclear to me from your comments whether or not you agreed with this, since you were questioning it so strongly, and I wasn't really sure where you were coming from. Re-reading it all now, I see how you meant your comments -- as a serious inquiry into the origins of gender, not as an attempt to dismiss it. My apologies on that. It is clear to me now that you are at least as knowledgable on the subject of language as I am, a fact which I welcome. Also, I was probably just being generally defensive, since I've been in many discussions in which people actually do hold to the idea that language is an "invention" consciously planned out by a few ancestral geniuses.
Anyway, back to the main question. I've been doing a little reading and have a few thoughts.
Did they or the original thing from which they descend once actually matter to the function of communication?
I believe that it did. I'm not sure how strong a case I can make for it, but I can think of ways in which it might be useful. Let's put aside the common male/female/neuter system for a moment and consider some of the other gender systems out there. The most basic is animate vs. inanimate (see interesting side note at bottom). There are 4-class systems with animate, inanimate, edible, and other objects. There are other languages with up to 16 different genders denoting categories such as hunting weapons, metal objects, dogs or other domesticaed animals, objects that are dangerous, etc. Some of the categories can be a little strange to our sensibilities. But I think the important point is that these categories, at some point in the history of the language, reflected things that were important in the environment in which its speakers lived, and the things that were important to their survival and well being.
Think about a hunter-gatherer society that speaks a language with a simple animate/inanimate distinction. One hunter says to another, "hey, look at that! Behind you!" In English, that doesn't tell us much. But if the pronoun "that" is inflected for gender, and it indicates an animate object, then that could be useful information. After all, it could be a lion creeping up on you. On the other hand if it's inanimate, you're probably a little safer
not engaging your flight-or-fight instinct and wasting energy. You may ask why the first hunter didn't just say "look, there's a lion behind you!" But that puts limits on the language; it makes it almost necessary to use the actual noun every time instead of being able to use pronouns (which are themselves an aide to speaking minimally, as you said). Also, it could be an unfamiliar animal and the hunter might spend precious time struggling for the right noun; in that case a quick "look at that (animate object)!" might be the best choice.
If you don't find that convincing, then perhaps I didn't choose a good enough example. But that's the
kind of thing I have in mind for the early function of gender.
Another possibility, not inconsistent with the above, is that the functionality of gender was largely a
social functionality. It expressed how a particular social group understood and categorized the world, and that expression, in and of itself, may have had some usefulness in helping the members of the group to bond and to share the same worldview. This could have been much more important in earlier "primitive" societies in which survival depended upon group cooperation.
SIDE NOTE: It is thought that Indo-European had a two-gender system (animate vs. inanimate). But most of its daughter languages have the more familiar male/female/neuter. It has been theorized that the original animate class morphed into male and the inanimate class split into two, female and neuter. Kind of shows you how women were viewed in past times, doesn't it?