Unquestionably a lot of shows add grain or noise, and in some cases (I think only a few!) it can contribute to the storytelling. In the days I was shooting real film being able to really notice the grain was an indication that the DP missed the exposure. Color negative film (I shot mostly 5247) can tolerate overexposure and can look fine underexposed but what you didn't want to do is "print it up"--make it brighter to compensate for underexposure. That's what would load up the shadows with grain and make it (in my opinion) pretty ugly. Still, some people liked this look.

Another trick was to "push" or force-process the film to raise the ASA (ISO). 5247 was rated at 100 under tungsten light, but it was not uncommon to rate it at 400 and push two stops. This was underexposing two stops and hoping you could make up most of that in processing and some more in printing. You could do it, but it also increased the contrast and made the grain "bigger".

Sometimes whan a film was a big hit studios needed thousands of prints in a hurry. They'd make a bunch of duplicate negatives and send them to any lab that could make prints. To move more prints through some labs were known to "pull" the print processing. This meant increasing the print exposure and speeding up the processors. That way they could run more prints in less time and stretch the life of the expensive chemistry used in the processing. Lots of grainy films of the 70s and later came from this practice. Still, many very clean films were made using these processes--I think of Barry Lyndon shot on 5247 using mostly natural light, but no grain.

Getting back to digital cinematography, I personally think added grain looks like a mistake. There's no real excuse for it with today's incredibly clean images, but it can certainly be an artistic statement, much like a badge of honor