It's funny how many decades we were striving to resolve the flaws in film photography and videography, only to get everything we wanted and then turn around and find a way back. Digital footage — particularly from the best cameras on the market, is characterized by incredibly clear, sharp, and clean footage. While that has always been the aspiration of the industry, now we miss some of the grain and character of shooting on film.
In fact, with all the latest and greatest digital cameras we have, flagship blockbusters are often shot on film. Take Oppenheimer for example, which was shot on a combination of IMAX 65mm and Panavision 65mm film stock. This is partially due to the enormous resolution that can be achieved with 65mm film stock, but also because the entire aesthetic has something appealing about it.
Although it is not a perfect replica, there are ways to create similar characteristics with digital files using LUTs. If you're interested in how it's best done, this video by Film Riot will explain.
One issue with adding film grain and other random imperfections to digital recordings, is that it greatly increases the bit rate needed to maintain fine details when there is motion. If you look at streaming platforms like netflix, amazon prime video and many others, if a movie uses film grain, you notice more compression artifacts, especially during motion, and for many free platforms like tubi, the heavy compression wreaks havoc on those movies while looking fine for ones that don't add much in the way of film grain.
I highly doubt fake film grain plays a big part in compression artifacts. Bitrates vary from service to service and content to content and possibly time of day. For instance, Netflix's content bitrate seem to range from 4 to 18 Mbps. Apple TV can go up to 40 Mbps. So, to blame film grain is pure conjecture since the only way to really know for sure is to have the same content (1 with grain, 1 w/o grain) on the same service provider streaming at the same bitrate during the same time.
I used to watch action movies from Netflix and Amazon on my 62" TV and never noticed compression artifacts during action sequences.
As for Tubi, they only stream max 720p at about 2.5 Mbps. I don't notice compression artifacts on my laptop 13.3" (2560 x 1600). It's more than fine. There's no wreaking of havoc.
From streaming there is no way to really do an AB comparison if dealing with a movie with added film grain, though it is something you can test with a basic camera and davinci resolve.
Record a well lit video so that the base ISO can be used, and pan the camera wide to side quickly, then export the video as h.264 5 Mbps (then add a node with film grain and then export again, then examine a still frame from the video in the middle of a pan.
You can also replicate it with a jpeg, Take any clean raw file (20MP or better) that you have captured before (base ISO and as little noise as possible). Export the image as a jpeg targeting a size of 5MB, then in photoshop add some film grain, then export the image again but adjust the compression to achieve a 5MB file again, then compare the resulting quality.
Beyond that, as good as compression has gotten, even with h.265 and AV1, they can't they can't detect noise and grain and treat them as details less worthy of preserving.