My point isn't about "graphics acceleration" (and the OP doesn't use that term either. It's about reducing memory bandwidth between from the CPU to VRAM.
The huge emphasis that ID guys put on reducing overdraw to basically nothing really helped it run on relatively shitty platforms. The basically optimized it to the point where CPU->VRAM bandwidth was the bottleneck.
Due to the algorithm it was double buffered, but all rendering calculations were definitely done on the CPU and the graphics device used as a framebuffer. So having a fast processor was critical for DOOM.
It was really only in the post-3dFX era that processors became irrelevant, and then only until physics modelling caught up.