  We observe Thurston's asymmetric metric on Teichm\"uller space may be
expressed in terms of the H\"older regularity of boundary maps. We then
associate $2$-dimensional stratified loci in $\mathbb{RP}^{n-1}$ to
$\text{PSL}_n(\mathbb{R})$ Hitchin representations with $n > 3$. We prove that
measuring the relative H\"older distortion of these loci gives asymmetric
metrics on the Hitchin component $\text{Hit}_n(S)$ with complete and
geometrically meaningful symmetrizations. These are the first known
geometrically significant complete metrics on $\text{Hit}_n(S)$ for $n > 3$.
