It is not clear how to define a map $\operatorname{Log}\colon X^{\mathrm{hyb}}\to\varprojlim_{\mathcal{X}}\Delta({\mathcal{X}})$, since each tropicalization map $\operatorname{Log}_{\mathcal{X}}$ is only defined on $X_{{\mathbb{D}}^{*}(r)}$, where $r=r_{\mathcal{X}}$ depends on ${\mathcal{X}}$. See §4.6 for a substitute in the projective case.