Why isn't the 'Crisis in Cosmology' or 'Hubble Tension' explained by the Accelerating Universe?

Both experiments report $H_0$, the Hubble parameter at redshift $z=0$, now. The different experiments directly measure $H(z)$ at different $z$'s then use the standard model of cosmology to determine $H_0$.

Late time or local measurements, like those using Type Ia supernovae and a cosmic distance ladder, measure $H(z)$ for small $zsim 1$. Early time measurements, like the CMB observations, measure $H(z)$ for large $zsim 10^3$.

There are two likely ways to resolve the differences between the two classes of measurements. First, one or both measurements could have unaccounted for systematic errors. In that case each experiments' directly measured $H(z)$ could be incorrect. When they calculate the implied $H_0$ the input would be wrong, so the reported $H_0$ would be incorrect too. Second, the standard model of cosmology could be incomplete. In this case each experiment is correctly measuring their $H(z)$, but the comparison at $H_0$ is flawed.