We don't use obvious grain, usually. That's generally precisely to evoke something about the past -- for flashbacks, a period look, etc. A sense of grittiness like 70s movies, etc.

On the other hand, a small amount of constant grain or noise is intentionally often introduced because otherwise images feel too static and end up looking almost fake. Similarly, dithering is intentionally added to audio, like mastering CD's or tracks. It helps prevent artifacts in video and in audio.

Even modern cameras have grain. If you need to integrate your scene with motion graphics, background replacement, or vfx, you'll need to remove grain on part of the image, edit it, add the original grain back where possible and synthesize new grain elsewhere.

Often it can also make sense to modify the grain for aesthetics. Denoising usually produces a less detailed result, but what you can do is denoise only the color channels, not the brightness channel. Brightness noise looks normal to us, while color noise tends to look very artificial. But by keeping the brightness noise, you avoid losing detail to the denoiser.

Same reason why movies still use extremely low frame rates - because people have gotten used to that effect.

It doesn't help that a lot of great movies are older thus those limitations of older technology become subconsciously associated with quality.

...what makes the frame rate thing especially weird is how many TVs ship with motion smoothing enabled by default, which looks so much worse than actual high frame rate content would.

I don't like it at all. But someone must, or the TV manufacturers wouldn't do it.

Part of me thinks that it's only the people who know what "frame rate" means who prefer low frame rates, and a majority of the general public actually prefers high frame rates but lacks the terminology or knowledge to express this desire.