Attrition works -- so why do we need amnesty?

But if illegal immigrants are going home on their own, why do we need an amnesty? The argument for it is that the illegal immigrants are firmly rooted here and aren’t going anywhere. While that’s probably true for some illegals, it’s obviously not true for lots of them. So why not wait and see how much more the illegal population can be reduced through attrition before we surrender and declare an amnesty?