Accurate screen emulation is important for many retro games, and not just because of color issues. For instance the GameBoy didn't support transparency so some clever devs would make sprites blink very fast to make them appear transparent. Since the GameBoy screen had a fairly slow response time the ghosting would effectively blend the sprite with the background. If you emulate the game on a modern low-latency monitor you just get a flickering sprite. See for instance the claw's shadow in this gameplay video for Link's Awakening: https://youtu.be/UQlP9sHf5Ho?t=825 (although this video is way worse that what you'd see in an emulator because the framerate of the video doesn't line up with the GB's ~60fps display, so it doesn't even flicker all the time).

An other example is games using the blurriness of analog video signals to blend things together: https://www.retrorgb.com/hd-retrovison-shows-transparency-co...

Basically you interlace two images at a high enough frequency and let the analog artifacts blend them. Once again doing playing that on a modern LCD screen without post-processing ruins the effect.