The way that rust attempts to prevent this class of error is not by making an implementation of free that is safe to call twice, but by making the compiler refuse to compile programs where free could be called twice on a pointer.

Anyway, use after free doesn't depend on a double free. It just means that the program frees memory but keeps the pointer (which now points at memory that could contain unrelated data at some future point in time) and if someone trying to exploit the program finds a way to induce the program to read or write to that memory they may be able to access data they are not expected to, or write data to be used by a different part of the program that they shouldn't be able to

Not really, the issue is that C/C++ is not memory safe, i.e. it allows you to access memory that has already been freed. Consider the following C++ code:

int* wrong() {
  int data  = 10;
  return &data;
}

If you try to use it it looks correct:

int* ptr = wrong();
std::cout << *ptr << std::endl;

That will print 10, but the memory where data was defined has been freed, and is no longer in control of the program. Meaning that if something else allocated that memory they can control what my program does.

Consider that on that example above later in the program we do:

user.access_level = *ptr;

If someone manages to get control of that memory between when we freed it and we used it they can make the access_level of the user be whatever they want.

This is a problem with C/C++ allowing you to access memory that has been freed, which is why C/C++ programmers need to be extra careful.