Why can't local variables be stored at fixed memory addresses?

Because recursion and re-entrancy need a separate copy of the locals per invocation — fixed addresses would let an inner call overwrite the outer call's variables.

Consider a recursive function with locals i and j:

int foo(int n) {
    int i, j = 0;
    for (i = 0; i < n; i++)
        j = j + foo(n - 1);   // recursive call
    return j;
}

If i and j lived at fixed addresses, the recursive foo(n-1) would write to the same memory the outer call is using, corrupting the outer loop's counter and result.

The stack solves this by giving every call its own frame:

foo(3): i,j at -4(%rbp),-8(%rbp)   ← one %rbp
  foo(2): i,j at -4(%rbp),-8(%rbp) ← a DIFFERENT %rbp
    foo(1): ...                    ← yet another %rbp

Each invocation has its own %rbp, so the same offset -4(%rbp) names a different physical location at every level. This per-invocation storage is exactly what makes recursion (and thread/signal re-entrancy) possible — and it's why "automatic" variables behave the way they do in C.

Go deeper:

• Recursion (Wikipedia) — recursion is why per-invocation local copies are needed.
• Call stack (Wikipedia) — per-invocation frames give each call its own locals.