Why does C++ not allow inherited friendship?

Because I may write Foo and its friend Bar (thus there is a trust relationship).

But do I trust the people who write classes that are derived from Bar?
Not really. So they should not inherit friendship.

Any change in the internal representation of a class will require a modification to anything that is dependent on that representation. Thus all members of a class and also all friends of the class will require modification.

Therefore if the internal representation of Foo is modified then Bar must also be modified (because friendship tightly binds Bar to Foo). If friendship was inherited then all class derived from Bar would also be tightly bound to Foo and thus require modification if Foo‘s internal representation is changed. But I have no knowledge of derived types (nor should I. They may even be developed by different companies etc). Thus I would be unable to change Foo as doing so would introduce breaking changes into the code base (as I could not modify all class derived from Bar).

Thus if friendship was inherited you are inadvertently introducing a restriction on the ability to modify a class. This is undesirable as you basically render useless the concept of a public API.

Note: A child of Bar can access Foo by using Bar, just make the method in Bar protected. Then the child of Bar can access a Foo by calling through its parent class.

Is this what you want?

class A
{
    int x;
    friend class B;
};

class B
{
    protected:
       // Now children of B can access foo
       void foo(A& a, int n) { a.x = n; }
};

class D : public B
{
    public:
        foo(A& a, int n)
        {
            B::foo(a, n + 5);
        }
};