That grain is an analog artifact is a correct statement.
I never commented on that section of your statement.
Whether it was added intentionally or not depends, in part, on when the movie was made.
Early B&W and early color film (not Technicolor, which was processed from three strips of B&W film, but real color film) had much more grain than modern film does. When movies were made and grainy film was the only thing that was available, I would argue that the artifact was not intended - it was just the best that could have been done with the technology that was available at the time.
Intentionally distorting an image can be an artistic decision (remember the color shifts in "South Pacific"), but in most old movies, grain is there by default - not by intent.
If the Director, DP, etc. were to make the same film today, and had more modern film stock to choose from, it's very possible they might choose a film with a finer grain. I'm not arguing that...
However, they made the film when they did, and they had what they had. I'm bad at analogies, but that's almost like someone back in the 60's complaining that they'd love their brand new Corvette, but it doesn't have a six-disc CD changer, keyless entry, and navigation system.
I've seen some examples of Blu-ray in which the time and care was put into the film to clean up the elements of unwanted noise (trash, marks, etc.) and dial down the grain, and the finished product was amazing, and I've seen films in which the picture was completely ruined.
Grain is not a bad thing. It is a PART of the films we love...