Why doesn't `std::initializer_list` provide a subscript operator?

Suppose that you are writing a function that accepts an std::initializer_list called list, and that the function requires random access to list's elements. It would be convenient to write list[i] instead of list.begin()[i]. So why doesn't std::initializer_list provide a definition of operator[]?

I can't think of any cases where an operator[] returning const T& would not be well-defined. Efficiency doesn't seem to be the issue here, since std::initializer_list<T>::iterator is aliased to const T*, which is clearly a random-access iterator.