The first PS3s had both the Emotion Engine and the Graphics Synthesizer of the PS2 inside them, which offered the best compatibility because it basically had a PS2 inside it. The last versions that had PS2 compatibility only had the Graphics Synthesizer of the PS2, resulting in poorer PS2 compatibility.

The current versions have neither th EE or GS in them, leading to no compatibility. Sony probably figured it was too difficult to program an all-out software emulator for it, even though there are PS2 emus that will run on decently specced PCs now.