The natural interpretation of a const constructor is that it constructs a const object directly. Such a constructor could eg. initialize a field declared with a mutable type using some external const reference.

void foo(const(int[]) a){
    // ...
    struct S{
        int[] a;
        this()const{
            this.a=a;
        }
    }
    // ...
}

The DIP argues that such a construct is not particularly useful

and hence eliminates it for the purpose of using the syntax for a _different_ concept. There is no way to implement the above constructor using the new semantics.