You do get the surprising result that if you have a child, you can’t call foo, but you can cast it to a base and then call foo.
child *c = new child();
c->foo; // compile error (can't access private member)
static_cast<base *>(c)->foo(); // this is fine, but still calls the implementation in child
I suppose you might be able to contrive an example where you don’t want a function exposed, except when you are treating it as an instance of the base class. But the very fact that that situation pops up would suggest a bad OO design somewhere along the line that should probably be refactored.