Huh, i didn’t know that about the psx polygon rendering.
That explains that janky amateurish quality a lot of the games have.
Just a quick short reply, so apologies for anything inexact, wrong term usage or misleading/confusing points. The main thing everyone notices about PS1 games is that when the camera moves the textures "swim" or move and that often the entire scene seems to judder and be on the verge of breaking up.
When Sony designed the PS1 it was before we had any real gaming industry 3D standards about how to display polygons, apply textures, etc. So Sony built the GTE to render lots of polygons really fast. Some of the shortcuts in things like where numbers are rounded or whatever resulted in this janky look. Some developers found ways to minimize the effects through careful texture usage or checking z-fighting or whatever. But others would basically just get the game up and running and not bother because it often wasn't worth the extra resources needed to do it. So it's usually in Sony second-party or big budget games.
Even in emulators you still see these problems, although a few have tried to fix them, because the basic problem is essentially in the math used originally and there's no way to recalcuate to get a more accurate number. IIRC one of the emulator plugins tried to fix the textures thing by having the modern GPU redraw the entire frame from scratch being sent the PS1 data. The modern GPU will go "woah, hey buddy, your polygons are messed up, lemme try and fix them first" but this can increase the emulation errors.
You can see the same kind of texture warping or polygon breakup in some early 3D PC games that predated the OpenGL/DirectX standards. Especially in their software modes. The Saturn doesn't "fix" this, and it can be seen in some games, but because it uses quads it changes how polygons meet which resolves a number of the more blatant issues. The N64 doesn't have really have these problems because it was more or less based on SGI's standards which wouldn't allow it.
The PS2 actually has some similar issues with its polygon setup but almost no games shipped with it not fixed or at least hidden. I do believe some of the Japanese launch window games can sometimes show it, along with the more infamous jaggies and shimmering that were actually related to this, since a lot of them had really really short dev cycles with no polish time before launch.