And again here's your key mistake -- no, you are wrong. Unfiltered textured polygons, at the resolutions and power levels 5th gen console run at, are pixelated. This is exactly why Nintendo decided to have texture filtering on the N64, to reduce this issue. It worked. The result was blurry textures, but again, the choice that gen is blocky or blurry, pick one.
The early N64 techdemo video here:
https://www.youtube.com/watch?v=eKlbx5niBu8 shows what I'm talking about. Of course the video probably overhypes the system, the kind of thing that got people expecting that the N64 would look better than it did once they saw games like Cruis'n USA and were disappointed, but "there are no blocks" are the point. To simplify, pixels are blocks. Nintendo 64 smoothing hides the blocks. The quality of the results depended on how good the development team was, but that was the goal anyway.
What would you say, that Nintendo only focused on that pre-release because of the hardware having limited texture cache? I don't think so, if Nintendo thought that the cache was such a big deal they'd have surely increased the size of the cache. That they focused instead on smooth textures shows their focus on getting rid of that blocky look. Not everyone likes the results of course, but that was what they did.
One of the best-looking games on the PS1 is Wipeout 3, that game looks a lot less pixelated than PS1 games usually do probably because it runs at a higher resolution than most PS1 games. The heavy use of texture that have only a few colors (solid or shaded or that sort of look) also surely helps. Anything shaded, of course, isn't going to be pixelated. And the game does have popping polygon issues because of the PS1's lack of perspective correction, of course, though they minimize it versus other PS1 games.