Reportedly, the only location to store textures for quick GPU read access was a whole 4 KB in size. What an, apparently, dumb mistake. The blur was bad.
Ps1 also only had a 4KB cache but it could also dynamically manage it for larger textures but that came with a large performance penalty.
The blur on N64 was a combination of that and small cartridge size. It graphics setup did have some advantages, look at Mario 64 for example. The hills in the distance are usually just a few polygons with some low resolution textures stretched over them. The filtering and perspective correction means it is a very consistent image, you would not be able to do that on PS1 without it becoming a visual mess.
PS1 affine rendering was fast but limited, which for the release window was good enough.