Why can't operator () of stateless functor be static?

Per standard 13.5/6,

An operator function shall either be a non-static member function or be a non-member function and have at least one parameter whose type is a class, a reference to a class, an enumeration, or a reference to an enumeration.

Additionally, in 13.5.4 it is stated that

operator() shall be a non-static member function with an arbitrary number of parameters. It can have default arguments. It implements the function call syntax postfix-expression ( expression-list opt ) where the postfix-expression evaluates to a class object and the possibly empty expression-list matches the parameter list of an operator() member function of the class. Thus, a call x(arg1,...) is interpreted as x.operator()(arg1, ...) for a class object x of type T

I would think that there's no technical reason to forbid this (but not being familiar with the de-facto cross-vendor C++ ABI (Itanium ABI), I can't promise anything).

There's however an evolutional issue about this at https://cplusplus.github.io/EWG/ewg-active.html#88 . It even has the [tiny] mark on it, making it a somewhat "trivial" feature under consideration.

I can't see any technical reason to forbid a static auto operator()( ... ). But it's a special case, so it would complicate the standard to add support for it. And such complication is not necessary, because it's very easy to emulate:

struct L
{
    static void func() {}

    void operator()() const { func(); }

    operator auto () const
    { 
        return &L::func;
    }
};

See Johannes' answer for some possibly useful extra info.