I had always wondered: If the famously-unlabeled buttons on the TOS bridge had been labeled, would those labels have been visible? In 2005, I did an experiment during the filming of "In A Mirror, Darkly" (ENT). For this experiment, I had hundreds of small clear labels printed with small numeric codes. I asked Alan Kobayashi to stick them onto most of the backlit "jellybean" buttons on the re-created TOS Enterprise bridge set, thereby labeling each button. Those labels were on the buttons when the episodes were filmed. When seen on screen, those labels disappeared completely. In other words, while the labels were visible to someone sitting at each console, when you saw them on screen, you could not tell that they were labeled. So, my theory is that the buttons on the "real" Enterprise bridge are indeed labeled, but you couldn't see them.
BTW, I had a similar thought during "Encounter at Farpoint," the first episode of Star Trek: TNG, in which I did not label most of the small buttons on the Enterprise-D bridge because I thought they'd never be visible on television. After seeing the first TNG episode on screen, I decided that I might be wrong, so (after consulting Bob Justman) I gradually added alphanumeric codes to all the buttons on the TNG bridge.