Huh, I didn't know that's the case for x86. My quick search suggests that support is still quite limited though, and none of my HW (1~4 yrs old) support it. I suppose by the time the spec is finalized and widely adopted HW-accelerated SHA256 would be, too (and I should switch my zfs checksum back from SHA512/256 to SHA256).
I haven't found any Intel hardware with the SHA extensions actually implemented. I was expecting it in Skylake but apparently that's not the case... Not sure when we can expect to see them.
Right now the most common x86 CPU which implements the SHA instructions is AMD's Ryzen. The only available Intel CPU which supports them is Goldmont, the latest generation of Atom CPU. It seems likely that Cannon Lake and possibly Coffee Lake will also implement them, but I haven't seen any rumors pointing one way or the other.
SHA-3 is just Keccak with specific capacities. If you mean that they should not implement only the standard SHA-3 functions then I agree, having c/raw/SHAKE256 as well would be nice.