24 fps was the capture rate of old film cameras. The reason for that is because of how sound was stored on the edge of celluloid tape. Because of how the sound waves where imprinted on the tape, the max fidelity was at sample rate of at most 10,000 Hz per 18inches of tape. So, 18 inches of tape has to move through the projector and sound head every second.
Consider a 35mm film reel which was popular at the same time. On a 35mm reel, the height of a single frame is about 19mm. So we have 18 inches (457mm) going across the projector screen, which shows a new frame of film every 19mm. That tells us the frame rate: 457/19 = 24.
And that is why films run at 24 fps. Because it was the natural result of technical constraints when sound started being added to film. This is why older silent movies could use lower frame rates. Super 8 cameras recorded at 18fps because they could get away with it, but once Sound Super 8 hit the scene, it got brought back up to 24fps for much the same reasoning as the 1930s had with 35mm film.
Hmm… I’m detecting that we may be operating with different definitions - made no more clear by the fact that you are talking about projectors while I’m answering a question about cameras. To me, a frame is a single still image on a reel of film.
I think I see your point that a projector would insert more black transitions from on frame to the next so that the black transition from one frame to the next isn’t as noticeable. However, I don’t see the connection to original discussion about frames per second or where the film industry standard of 24fps came from.