The problem I see with these analyses is that they try to drag in a bunch of additional facts to produce some kind of "just-so story" based on how a beard protects from cold or a smack to the face. A posteriori explanations are always suspect. And they always focus on "how does it benefit the individual man in question?" What about "group fitness" and how could that work? What are the facts? 1. humans are hairless almost everywhere else, 2. beards appear at the onset of sexual maturity. And another couple of obvious but oft-neglected fact: 3. women and young children remain beardless, 4. men's voices change with puberty. Taking a shallow dive into a semiotic and macromemetic examination of the facts, and how a beard "disrupts" the environment, we see that as soon as men mature, they immediately become visually distinct from women and children. Oh, and facial hairlessness is a feature of neoteny, of course, and it's a fact that the human brain is attracted to and prone to display altruism towards faces that seem "childlike." And their voices change (become lower). Note that we haven't asked "why?" about any of this yet--let's keep it objective. Another fact: a high-pitched sound has more "penetrating" capacity, it can be heard over longer distances and over other background noise (it has higher energy for the same wave amplitude). This is just basic physics (which any sound engineer knows). Thus, we can say, just based on the facts, that when human males reach sexual maturity, they move out of the class of neotenous, attention- and altruism-attracting, cries of pain and alarm more attention-getting tribal members. Who knows what this means? But it is a simple conclusion based on the simple facts that we definitely know.
Now, we can maybe start to speculate along sexual selectivity lines. Women and children are highly valuable to the survival of the society/tribe, while the loss of even a large number of mature men can be replaced, in fact, a man's ability to survive is one of his most valuable (reproductive) traits, only measurable if many other men die off around him. So the ability of a given population to do a better job at clearly marking (visually and by vocal cues) which members are high-value and which are expendable (able to defend themselves or die trying) would presumably do a better job of thriving over time, i.e., women and children would have a higher rate of survival. You could also posit that by the same token beards allow men to quickly recognize each other, either as fellow expendable fighters and defenders, or as "permissible" rivals that one can choose to fight (to the death).
So the semiotic take is that a beard is a "sign" that a man is expected to defend himself, or defend the women and children, or be considered an eligible rival in fights for hierarchical prominence. In macromemetics this would be a MIAO (Memetic Iconic Anchoring Object), serving the same sort of function, i.e., eligibility to participate in some social functions and not others.
Now, if you want to take the "group fitness" concept to the next level, i.e., "super-group fitness," and the idea that mature men are expendable compared to women and children, we could look at competition between tribes/cultures. Now men in a tribe under attack by another are clearly marked (a macromemetic concept, by the way) as targets to be killed outright, and all non-bearded enemies are to be captured, not killed, if at all possible. Obviously, from a species fitness perspective, for a warlike species like ours, immediately knowing which individuals to kill and not to kill (facial hair means kill, no facial hair means leave alive...probably...more on this later). Again, clearly, and to an even greater extent, having a beard would not serve the man who wears it at all, quite the contrary, but may provide great service to the species as a whole.
Okay, we took the facts and made some obvious conclusions, i.e., that beards keep women and children "prominent" which is kind of an "anti-advantage" for individual mature men, but possibly a big advantage for a single tribe and potentially a very big advantage for the species as a whole against the backdrop of our warlike nature. These present some theories for anthropologists to work on, which could inform geneticists and biologists as to how the pattern of human male puberty developed.
One final thing: "Shaving as Technology."
Obviously, shaving defeats the selectivity afforded by the bearded male face. We can put forward some more advanced theories for the anthropologist and historians to really sink their teeth into. How does this impact misogyny and gender politics? How does it impact military rivalries between cultures? This is getting rather advanced, folks, and starting to really reach into some areas that need a lot of research before anything definitive may be proven, so don't let it warp your impression of the foregoing, really obvious stuff based on the basic facts. Were the Greeks able to slaughter the Persians wholesale while the bearded Persians were "confused" by the Greeks' shaven faces, giving the Greeks an advantage? The Romans? How do beardless men "confuse" women and other men in societies that have shaving? What about cultures where shaving was looked down upon (and how? bare-facedness is "womanly" and therefore bad?)? Do cultures with widespread shaving tend to be more, or less, misogynist? Or will historians and anthropologists find it not to be a factor? Do men who have no beard somehow "trick" society into viewing them differently? What does this mean?
Anyway, to paraphrase JFK, "Ask not what your beard may do for you, ask what your beard may do for your country."
Again, the semiotic/macromemetic approach is simply to look at what the presence or absence of a beard does in the environment, including with those who continue NOT to have beards always (anti-sign/MIAO).