Engine compromise: The Sims on PS2 uses a custom engine that downsamples textures and applies a slight blur/dither to mask low-res assets and aliasing on composite/CRT output.
No modding pipeline: PS2 homebrew (FreeMCBoot, OPL) cannot patch in-game rendering shaders for retail discs.
Mitigations (Minimal Effect)
Component cables (YPbPr) + progressive scan (480p): If your game supports it (hold △+✕ at boot), sharper image reduces perceived fuzz.
CRT TV: The "fuzz" was partly intentional dithering for CRT phosphor blending. On modern LCDs, it looks worse.
Emulation (PCSX2 on PC): Upscale to 1080p/4K, enable texture filtering, widescreen patches. Best visual quality by far.
Embrace the retro look — it's part of the PS2 era charm. For crisp Sims, play The Sims 2/3/4 on PC.