Also, they fix a lot of the issues that early game consoles had.

For example, affine texture mapping and the pixel popping that really gave the PSX its distinct flavor is completely gone from modern games that try to emulate it. Or the SNESes texture warping in mode 7. Or the N64s very monotonous textures (or essentially black and white video due to compression).

If a game really tried to replicate the PSX or N64, I don't think people would like the result. Modern sensibilities appreciate the idealized aesthetics, but not the rough edges.