Using Anderson localization as an example, I understand how scale invariance comes into play at a critical point - at a critical point, the localization length $\xi$ (the average "radius" of the eigenstates) diverges, so that if one "zooms out" then the system looks the same, because any finite rescaling of infinity is still infinity.
What I don't understand yet is why the same could not be said beyond the critical point. For example, suppose that below the critical disorder $W>W_c$ my system is localized, and above the critical disorder $W<W_c$ my system is extended. The localization length $\xi$ is finite for $W>W_c$ and infinite for $W<W_c$. Why don't we say that the entire extended phase $W<W_c$ is scale invariant? After all, $\xi$ is still infinite, so that the system will still look the same if we zoom out.
I would like to understand why the $W<W_c$ case is not considered scale invariant in hopes that it will help me to understand what happens in finite systems. I've seen simulations of finite systems with two parameters, disorder $W$ and system size $N$, for which the critical parameter such as $\xi$ is independent of system size $N$ exactly at $W=W_c$ but neither for $W>W_c$ nor for $W<W_c$. Since scale invariance occurs at $W=W_c$, the point where the critical parameter is independent of $N$ is identified as $W_c$.