I discuss a similar matter in post # 409 here:
Did you ever hear of a frame story? That is an almost totally obsolete storytelling technique used in old time stories like, for example, Frankenstein: or, The Modern Prometheus (1818), a short story that explains how the writer learned of the events in the main story.
When we read or watch a work of fiction, we suspend our disbelief and sort of kind of believe that the fiction is, in some sense, sort of real. But we don't forget about the real world. If the fictional setting of the story is too different from what we know of the real world there is a degree of need for an explanation for the differences.
If a story is set in the distant past, the frame story could be that an ancient manuscript telling the story has been discovered, or maybe that the writers read a bunch of history books written in ancient times that told the story. So if a story is set in the past, we can easily imagine a rather simple frame story that explains how the events are known in the present.
But if a science fiction story is set in the future, then the frame story that explains how events in the future became known in the past is itself a science fiction story involving time travel.
Since frame stories are rarely ever used, readers or viewers of science fiction stories set in the future are free to make up their own frame stories about how the future data became known in the present.
And such possible frame stories vary greatly in how much of what we see is "actually" true future data and how much is "actually" contemporary attempts to depict the future based on incomplete data.
On one extreme Star Trek episodes could be actual record tapes made in the future and edited in the present into episode or movie length. That would make them very accurate. On another extreme, Star Trek episodes might be based on mission reports from the future that were used to write teleplays, and all the visual and sound aspects of the episodes are contemporary attempts to depict the future and not really canon.
If Star Trek episodes and movies are record tapes of future events somehow sent back in time to our era and edited into episode and movie lengths, then the look of everything is 100 percent accurate and the differences between the appearances of the two sets of actors is a real problem to be investigated.
On the other hand, if Star Trek episodes and movies were produced in the ordinary 20th and 21st century way, but were based on future mission reports sent back in time to the present somehow, only the plot elements dictated by those 23rd century mission reports would be accurate and canonical and the looks of everything, including the appearance of the characters, would be due to 20th century TV and movie production and not canonical data.
For example, every stage, movie, or TV production of MacBeth is based on Shakespeare's play, and many of them have the exact same plot and dialog if they are totally faithful to the source play. But the actors, costumes, landscape, sets, and other visual aspects look different from production to production. One might say that the look of a particular stage, movie, or TV production of MacBeth is canonical in the universe of that particular production, but none of the visual looks of any production of MacBeth is canonical in the universe of Shakespeare's MacBeth as a written script for a play.
(And of course Shakespeare's play MacBeth is based on various history books available in his time, which were based on earlier history books, and so on back for five hundred years to the actual historical events which inspired MacBeth, though it would be possible to write a play that was far closer to the real history than MacBeth is.)
And it is perfectly possible to imagine a frame story for Star Trek in which many Starfleet mission reports and logs have been sent from the future into the present and are used as the scripts for filming episodes and movies based on the future history in those reports. So the Star Trek plots might be almost 100 percent accurate, just as the plots of most productions of MacBeth are faithful to Shakespeare's play, but the visual details - including the faces of the characters - would be more or less arbitrarily chosen by the 20th and 21st century movie and TV creators and not really part of the canon, any more than the appearances of the actors in a particular production of MacBeth are canonical to Shakespeare's play MacBeth.
The fact that there doesn't seem to be a discussion of the different faces of the characters in the reboot Trek indicates that the faces are supposed to be same and that visual details like the faces of the characters are not canon, and thus that the frame story of Star Trek is that reports were sent into the past, not actual visual record tapes.
The fact that the computer on Old Spock's ship seems to use facial recognition and voice print to accept new Spock, as pointed out by Kevin Laity, indicates that they have identical genes, including the genes that control voice and appearance, and thus their faces are supposed to be same and that visual details like the faces of the characters are not canon, and thus that the frame story of Star Trek is that reports were sent into the past, not actual visual record tapes.
Until and unless an example is found of a comment about different faces in New Trek and Old Trek the default assumption should be that the faces are the same in the story, and that the frame story of Star Trek is that reports were sent into the past, not actual visual record tapes.