Film wears out through repeated use. While a loop of film would have been theoretically possible, the tech to transmit it would have required just as much TV camera electronic equipment, plus a complex film projection device; the film would have gradually gotten scratched and picked up dust and worn out, and it would have had a great many failure modes.

In contrast, pointing a TV camera at a spinning globe was much easier. And for showing the time, pointing at a physical clock was much easier than, what, having twelve hours of film footage available and having to synch the right frame?

I think what’s maybe more surprising for people than that moving station idents were typically in camera props, is that broadcasting even a static image pre-digital was also much more easily accomplished by just pointing a camera at a piece of card - even repeating a single frame over and over again was not something that could be easily reproduced some other way; having a camera continually capture and immediately broadcast the frame was just much easier.

Video tape, once it came in, allowed freeze frames but continually reading from the same spot on a tape caused wear so you couldn’t rely on being able to show a single frame from tape indefinitely.

Digital freeze frame machines that could capture a frame of video and repeatedly play it back from a memory buffer only started showing up in the 1980s.