As in stl containers, why can't we access a typedef inside the class from the class instance? Is there a particular insight into this?

When value_type was a template parameter it could help making more general code if there wasn't the need to specify the template parameters as in vector::value_type

Example:

class T {
public:
    typedef int value_type;
    value_type i;
};

T t;
T::value_type i; // ok
t.value_type i;  // won't work