One way to get an empirical handle on this question is to write a rasterization pipeline entirely in software and run it in GPU compute. The classic Laine and Karras paper does exactly that:
https://research.nvidia.com/publication/high-performance-sof...
An intriguing thought experiment is to imagine a stripped-down, highly simplified GPU that is much more of a highly parallel CPU than a traditional graphics architecture. This is, to some extent, what Tim Sweeney was talking about (11 years ago now!) in his provocative talk "The end of the GPU roadmap". My personal sense is that such a thing would indeed be possible but would be a performance regression on the order of 2x, which would not fly in today's competitive world. But if one were trying to spin up a GPU effort from scratch (say, motivated by national independence more than cost/performance competitiveness), it would be an interesting place to start.
Conversely, there is a lot of logic on a modern CPU to extract parallelism from a single thread, stuff like register renaming, scoreboards for out of order execution, and highly sophisticated branch prediction units. I get the feeling this is the main stuff you're talking about. But this source of complexity does not dramatically outweigh the GPU-specific complexity I cited above.