Been playing through the Ace Attorney games on the NDS recently. Even though I don't play much NDS stuff, I couldn't help but notice how oversaturated some of the colors looked.
According to this thread: https://forums.libretro.com/t/real-gba-and-ds-phat-colors/1540/190, the screens on the NDS are just as shitty as the ones on the GBA.
With the shader, the wood in the background is finally brown rather than piss yellow. Also skintones and other scenes look way more natural too with this shader.
I haven't played the HD release, but from looking at some screenshots, it looks to me that they just took the raw assets and never even bothered with how the colors are supposed to look. The redrawn art looks jarring anyway.