Why is std::hash not an overloaded function?

I'm guessing std::hash is defined as a template struct in order to avoid implicit type conversions done during overloaded function resolution. Is it a correct thing to say?

I mean, I would prefer to write

std::string s;
size_t hash = std::hash(s);

instead of

std::string s;
size_t hash = std::hash<std::string>()(s);

But I'm guessing there's a reason for why the standards committee has chosen the second option.