BTW, because of choices made for color TV, it's almost never actually 60 fps... it's 59.94. https://www.tvtechnology.com/news/whats-the-difference-betwe...

60 frames per second is because (in the USA) electricity suppliers standardised on 60Hz mains frequency, and in the early days of TV it was easiest to make the refresh rate match the mains supply.

(In the UK the mains frequency is 50Hz, as is the standard TV refresh rate)

Huh, that's certainly a more fundamental reason that the NES frame is that length...!

I wonder if people involved with early film and video had a lot of 60:1 gearing available because of clocks or something (or just thought it was a very intuitive division to use).

well 60 * 17 = 1020 (about as close as you can get to a millisecond with integers), so it lines up pretty well.