Why does C++ not have a const constructor?

Question

(Edit: Heavy change because previous example was flawed, which may make some answers/comments seem odd)

This might be an overly contrived, but the following is legal because of lack of const constructor:

class Cheater
{
public:
    Cheater(int avalue) 
       : cheaterPtr(this) //conceptually odd legality in const Cheater ctor
       , value(avalue) 
    {}

    Cheater& getCheaterPtr() const {return *cheaterPtr;}
    int value;

private:
    Cheater * cheaterPtr;
};

int main()
{
    const Cheater cheater(7); //Initialize the value to 7

    cheater.value                 = 4;    //good, illegal
    cheater.getCheaterPtr().value = 4;    //oops, legal

    return 0;
}

It seems like providing a const constructor a thing would be as easy technically as const methods, and be analogous to a const overload.

Note: I'm not looking for 'Image( const Data & data ) const' but rather 'const Image( const Data & data) const'

So:

Why is the const constructor absent in C++?

Here's some related material for context:

Why does C++ not have a const constructor?

5 Answers