It was definitely the process on the Jaguar. The Jaguar version is still using software rendering on the RISC CPUs. And just to put this to bed, here is proof that Doom on Saturn is using VDP1 to draw the walls, and that VDP1 is infact the choke point:
Doom With VDP1 disabled, VDP2 enabled:
https://i.imgur.com/VphLles.png
VDP2 disabled, VDP1 enabled:
https://i.imgur.com/WtN0d6z.png
So there you have it, Doom on Saturn IS using VDP1 to draw almost everything. Hexen runs better because it does the opposite. VDP1 draws very little, and VDP2 draws the bulk of it.
Warping is an issue on the Saturn too, it just happens a little differently. It happens more when polygons get closer to the edges of the screen.
Because those games do a ton of subdividing to try and hide it. And they target 30fps but usually have dips below that. They're not doing 60fps. The only way you'd be getting 60fps in an FPS would be if you were using huge quads to lower the number of quads being used, and that would result in a ton of warping. Again see this attempt at doing just that on the 3DO, which renders similarly to the Saturn:
https://www.youtube.com/watch?v=X_ytaHm7ABk
Look at around 6:30 when he turns on the polygon rendering engine. The doors really look bad with all that warping. I'd imagine that's close to what this fabled beta version of Doom looked like, if not worse.
I'd say take the whole account of how this fabled beta looked and ran with a massive dose of salt.
Take the time to read posts and understand what's being said then. Do you have any idea how exhausting it can be debating with you when myself and others have to keep repeating ourselves because you don't take the time to read something properly and jump to the wrong conclusions or put words in our mouths?
Hop on the SegaXtreme discord. There's plenty of people there who can help you get started if you want to tinker around.