Why doesn't the compiler perform a type conversion?

Consider the following code.

#include <iostream>
#include <string>

struct SimpleStruct
{
    operator std::string () { return value; }
    std::string value;
};

int main ()
{
    std::string s;    // An empty string.
    SimpleStruct x;   // x.value constructed as an empty string.

    bool less = s < x; // Error here.
    return 0;
}

This code does not compile either on g++ or Microsoft Visual C++. The error report given by compilers is no match for operator '<' in 's < x'. The question is why does the compiler not simply convert the SimpleStruct x to string according to the given operator string () and then use operator < ( string, string )?