Why is std::hash a struct?

If you check the C++ standard you will find that std::hash is a struct instead of a function. Reference is here.

It has the () operator overloaded so that we can use it just like a function (std::size_t std::hash()).

Why it is a struct?

Store meta information

I think the initial reason (before C++17) is that, struct can store meta information such as types for static deduction unlike function.

Before C++17, you can do:

std::hash<T>::argument_type // T type
std::hash<T>::result_type // std::size_t type

After C++17 you can use decltype(T) and decltype(std::hash<T>()) so these types are no longer needed.

Salted hash

Because it is a template struct, you can add member varibles in your type specification, such as seed value to enable salted hash.

Even the default specifications for all std data types are stateless, you can add hash states as well for your own application.

Salted hash also requires the std::hash to be created as a discret object to store the internal seed value, instead of being a conceptual function and never created in the software.

Conclusion

std::hash is designed to be a struct so that it gives the user more freedom to design the hash process.