You still need some privileged process to exploit. Glibc code doesn't get any higher privileges than the rest of the process. From kernel's point of view, it's just a part of the program like any other code.

So if triggering the bug in your own process was enough for privilege escalation, it would also be a critical security vulnerability in the kernel - it can't allow you to execute a magic sequence of instructions in your process and become a root, that completely destroys any semblance of process / user isolation.