No idea why 60 Hz on an LCD works better, though.

Because LCD pixels are constantly lit up by a backlight. They don't start to dim in between refresh cycles. They may take some time to change from one state to another, but that is perceived as ghosting, not flickering.

On a CRT the phosporus dots are periodically lit up (or "refreshed") by an electron beam, and then start to dim afterwards. So the lower the refresh rate, the more time they have to dim in between strobes. On low refresh rates this is perceived as flickering. On higher refresh rates, the dots don't have enough time to noticably dim, so this is perceived as a more stable image. 60Hz happens to the refresh rate where this flicker effect becomes quite noticable to the human eye.

60Hz is what any NTSC TV would have had for consoles. Plenty of older computers, too. Lots of people gamed that way well into the 2000s.

Incidently, if you do the same calculation above for PAL (50Hz), you end up at 10ms, or about 2ms more lag than NTSC. Many modern LCDs can have response times <2ms (which is on top of the console's internal framerate matched to NTSC or PAL). The implication for retro consoles is that the lag difference between NTSC CRTs and modern LCDs is about the same as the difference between NTSC and PAL CRTs.