Examples of "interesting" applications of that fact that $ACF_p$ is $\kappa$-categorical?

Question

In my Mathematical Logic course, we have discussed the fact that $ACF_p$ (algebraically closed fields of characteristic $p$) is is $\kappa$-categorical for $\kappa > \aleph_0$ in FO logic. I can see how this can be very useful in the field of pure algebra since it implies completeness of the theory- if I prove something FO for $\mathbb{C}$, I've proven it for $\overline{\mathbb{Q}}$! However, although using the completeness "feels" very interesting, it simultaneously feels verey restricted, since I can't even discuss "polynomials" in general within FO logic. My question is whether anyone has any non-trivial examples of FO statements that, say, can be proven $\mathbb{C}$ and thus hold for all $ACF_0$ fields (or a phenomenon of similar nature)?