This SNES video analysis one is incredible. I've always had all of this stuff running around in my head for how to explain how weirdly cool video generation for NTSC is, and you have done an incredible job finding a way to do so.
There is yet another reason for the weird frame and horizontal scan rate. When NTSC was originally introduced as a broadcast standard over a single RF modulated signal, the sound carrier and signals were also embedded in the signal as well. [1] Actually, I just found that Wikipedia does a good job of describing this on the NTSC page [2]:
When a transmitter broadcasts an NTSC signal, it amplitude-modulates a radio-frequency carrier with the NTSC signal just described, while it frequency-modulates a carrier 4.5 MHz higher with the audio signal. If non-linear distortion happens to the broadcast signal, the 3.579545 MHz color carrier may beat with the sound carrier to produce a dot pattern on the screen. To make the resulting pattern less noticeable, designers adjusted the original 15,750 Hz scanline rate down by a factor of 1.001 (0.1%) to match the audio carrier frequency divided by the factor 286, resulting in a field rate of approximately 59.94 Hz.
So yes, yet another difficulty with NTSC -- sound actually splattered visual noise on the screen as well!
A bit unrelated, but the links to your books at your website are no longer working. I tried to connect to you via email for this issue. Is this intentional or you will fix them?
It was originally 60 fields per second (30 interlaced frames per second), on black and white TVs.
The highest frequency generated in a black and white TV was the horizontal scan rate, which was a multiple of the frame rate. With the addition of the NTSC color signal, which used a 3.579545 MHz carrier wave, the highest frequency generated in the TV became much higher. To keep the hardware simple, all lower frequencies were still divisors of the highest frequency, now color carrier wave. For the frame rate, it came out to 59.94 fields per second.
No power grid I know of runs at 30Hz. North America (where NTSC was designed) and a few other places[0] run at 60Hz.
[0] https://en.wikipedia.org/wiki/Mains_electricity_by_country