Would replacing ' :: ' with ' . ' create ambiguities in C++?

Due to attempts to make C++ mostly compatible with the existing C code (which allows name collisions between object names and struct tags), C++ allows name collisions between class names and object names.

Which means that:

struct data {
    static int member;
};

struct data2 {
    int member;
};

void f(data2& data) {
    data.member = data::member;
}

is legit code.

An example where both are valid, but refer to different objects:

#include <iostream>

struct A {
    int i;
};

struct B {
    int i;
    A B;
};

int main() {
    B x {0, 1};
    std::cout << x.B.i << '\n';
    std::cout << x.B::i << '\n';
}

See live on coliru.

Let extend @Deduplicator example:

#include <iostream>

struct A {
    int i;
};

struct B : public A {
    int i;
    A A;
};

int main() {
    B x {1, 2};
    std::cout << x.i << '\n';
    std::cout << x.B::i << '\n';  // The same as the line above.
    std::cout << x.A.i << '\n';
    std::cout << x.A::i << '\n';  // Not the same as the line above.
}

Live on Coliru Viewer

Not having a possibility to differentiate with help of ::, which member we want to access, it is impossible to access members declared in a parent class with identical names.

There is difference between a::b and a.b where :: implies that a used as namespace, which means that it is namespace or typename. Provided that C++ supports non-virtual plural inheritance and that a variable can have same name as a type, this strips chances of referencing wrong object. It's necessary for template metaprogramming.

Another example would be &B::foo vs &B.foo in context of class B.