The Riemann-Hurwitz formula implies that the projective line $\mathbb{P}^1_K$ over any algebraically closed field $K$ is simply connected (i.e., $\pi_1^{et}(\mathbb{P}^1_K) = 1$; equivalently, if $\phi\colon C\to \mathbb{P}^1_{K}$ is finite etale, then $\deg\phi=1$). For $K=\mathbb{C}$, this follows from the connection with topology and from the fact that the complex plane $\mathbb{A}^1_{\mathbb{C}}$ is contractable. In positive characteristic the affine line is not simply connected due to Artin-Schreier covers.

My question is whether there is a short proof for this fact in positive characteristic?