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While it takes a hardware engineer to fully understand what's going on in their patent, relevant to the discussion is the following quote:
[…] certain portions of the input message, state data, and input values to multi-stage SHA-256 engines 110, 112, 114 may be fixed to constant data values during SHA-256 hashes or during certain rounds of computation in the SHA-256 hash. Rather than providing these constants using registers, embodiments of the present disclosure hardwire these constant data values to the circuits performing SHA-256 hash, thus reducing the energy consumption compared to providing these constants using registers that may be enabled by clock signals.
Intel researchers seem to have determined that there are no optimizations that can be made at "stage 0" of SHA-256 calculations, but that the other two stages, as they call them, have ample opportunity to be optimized.