Actually, your argument seems to point more towards that no one but Eowyn could actually kill the Witch King, since the terms of the prophecy are merely vague references to what someone actually knows about the future.

And to point things out from another viewpoint, a lot of the powers of any character come through machinations of plot. If we dismiss this prophecy merely because 'it is a plot device' then I'm sure we can dismiss a slew of Soth's powers, or many things about other threads such as this.