Most Japanese companies are not run like American companies. There is a deep culture of compromise and consensus over top-down leadership. One of the results of this is the need for every stakeholder in the company to have a hand in every decision, and to get a piece of every new product.

For the Saturn, this resulted in the console packed with little goodies that were created by different departments. Things like off to the side audio chips that did barely anything. Dual CPUs. Strange 3D tech that used quads instead of triangles.

A few years later, we did work with Sony, and they seemed for some reason to work more like an American company, in the sense that they say they need more able to make rational decisions and move quickly when they needed to.

No one who has worked for a Japanese company would ever use the word agile to describe them. Sony may be the exception, at least at that time.

It allowed for repurposing of sprite-drawing hardware the Japanese were already familiar with. Most Japanese programmers at the time were at complete sixes and sevens with the sort of triangle-based, texture mapping 3D hardware that had been developed in the west. I guess Sega thought it would be either a faster path to developer success, or easier to implement in hardware, if the Saturn's 3D engine resembled the sprites that game and console makers already knew, rather than gamble on unfamiliar triangle rasterization.

Nintendo collaborated with SGI on the N64, giving them a HUGE leg up on ALL the competition with respect to rendering techniques -- perspective-correct, filtered textures when even the PlayStation could only do affine transforms on textures (leading to the "texture warping" phenomenon). But even their programmers had to come to grips with 3D, which was hard. One reason StarFox 2 was cancelled was because Nintendo wanted to use its camera code in titles like Super Mario 64 (and did NOT want word of this getting back to Argonaut).

How do you even render a quad? What if it isn't planar? Does it curve or crease?

Their arcade boards used quadrangles too, not that that really answers the question

Sega had a lot of prior experience with quad-based 3D games. Their Model 1 and Model 2 arcade boards used quads.