I guess 32-bit x86 performance is maybe not the best benchmark. I think people aren't optimizing for that ISA to the same extent as they are optimizing for x86-64, 64-bit ARMv8, or 32-bit ARM.

If you care about performance and you don't have dedicated SHA-256 instructions then on a 64-bit platform you should evaluate SHA-512 as it is much faster. If you only have 256 bits of storage available then truncate its output to 256 bits. IIRC, it's about 1GB/sec on my Haswell laptop.