Wolfenstein's correct texture mapping is due to it using raycasting in a 2D plane and rendering scaled vertical strips of texture, which just happens to be perspective correct because you only ever have surfaces at 90deg angles in the vertical.
As to why those extra triangles weren't used for detailing, it's likely because that would take up extra level data. Tessellation of an existing triangle into smaller triangles doesn't.
Wolfenstein and Doom are 100% correct because Carmack 'cheated' by deciding to never look down/up or draw slopes :-) so whole game is drawn with 'lines of constant Z'. Or as they put it
Chris Hecker (Microsoft/Maxis/etc): that's a classic Carmack thing which is like Fuck those general problems, Im gonna solve this other problem perfectly
John Miles (ORIGIN/Miles Design/etc): Its all about not doing the math, we were still at a point in time when you won by not doing the math
Great link. The artifacts are especially apparent when the walls are near the camera, for example at this timestamp: https://www.youtube.com/watch?v=VutzIK3DqZE&t=398s And note that here, the seemingly flat walls are already heavily subdivided into smaller polygons to lessen the impact of the problem. (Why they wouldn't then make use of those additional polygons to include more geometry details for free is beyond me, however.)