CPS2 cases are ABS plastic. While some of the grime you’re seeing is actual dirt and possibly nicotine, it’s likely that the deeper staining is caused by the bromine in the plastic. This is just like you’d see in the cream plastics of the 80s and 90s (Amiga, Atari ST, SNES...) where they turn yellow.
I’ve heard of people using Retr0bright or similar peroxide cream methods on coloured plastics, such as an indigo GameCube, which apparently improved the appearance of the plastic without affecting the colour.
Obviously, there is the debate about the permanency of using such bleaching agents, as in some instances the staining may return. There is also a theory that using them can weaken the plastic, although in my experience, ABS can weaken over time anyway.
I’ve not tried it with CPS2 cases myself, I just live the the fact that the plastic will discolour as it ages.
I do think that keeping them in a cool environment will slow the discolouration more effectively that keeping them out of the sunlight; it’s just that generally, where there is sunlight, there is heat! I’ve had other plastics that have been kept in the dark, but they have still yellowed because of the heat.
If anyone happens to try Retr0bright/peroxide cream on a CPS2 case, I’d be interested in seeing the results.