For gradients it definitely isn't unless you have the ability to do FRC dithering where the dither pattern changes every frame. The banding is very noticeable on a large enough screen.
LG just introduced a new 13 bit color TV... https://youtu.be/82InNlCqxlU it makes a difference in dark colors apparently. I can often still see banding on high end monitors.
Do I need that kind of precision in my CSS? Probably not. But for gradients, it seems helpful.
Yes. The claim that you don't need more than 3 decimal places is laughable. Your artificial design doesn't need decimal points. At all. You probably can do even better by ignoring the last 4 bits completely.
That said, the article is very interesting, and that claim applies on different contexts. It's just aimed at the wrong one.
(It both is and isn't, depending on the use case, but I'm pretty sure nobody's design needs to make a difference between #123456 and #123457.)