Sonys biggest mistake with the PS2 was not getting the tools right before launch. Or indeed any reasonable time after that. If at all.
There was no real incentive to push the hardware because everything would sell reasonably well because of the insanely big user base. Everyone "knew" what it could do so a false floor or level of normal was created. Thus the machine was hardly ever pushed. Even the games that did dare to push the envelope hardly scratched the surface, being content to do a few things right and mostly be mediocre games otherwise.
The EE had an on-die macro block decompressor with insanely high throughput, much higher than would have been ever needed for playing a DVD. The intent was of course to decompress textures for games on the fly.
No one to my knowledge ever utilized that feature. With MIP mapping and decent culling the texture throughput per frame would never need to go above a few megabytes, when the frame itself was only one megabyte. Most likely it should have been less had 16 bit textures been used.
Huffman decompression was done by the CPU and VU´s for textures but why use precious time for that, when there is much better hardware with higher compression sitting right there?!
Geometry on the PS2 was meant to be synthesized. That much is clear from what Kutaragi said early on before release. The geometry was meant to be largely dynamic, instanced and generated on the fly. If that had been done more throughly PS2 games would have looked a hell of a lot better.
The MIP level could have been set for inclined surfaces or whole objects with approximately the same surface inclination towards the screen to avoid shimmer. Culling could have been done more effectively, and the triangles could have been generated to the right size to avoid thrashing the cache if too small and have texture jumping if too large, etc.
Doing stuff like that of course would have meant that the game would have been harder to port to other less advanced platforms. But who cares if the install base is so large?!
The real answer is I suppose that the computer industry is the most conservative, stiff and dogmatic of all the branches of engineering when it comes down to it. Double up for game programmers. ;-)
Why didn't even Sony use these techniques? I don't really understand but it sounds like a fantastic opportunity. They could have extended the life of the machine which was essentially printing money by then.