Comment on: "Questioning the $H_0$ tension via the look-back time"

Recently, it has been proposed that Hubble tension can be addressed in the $\Lambda$CDM model if the lookback time approach is considered on the redshift $z$ measured. From this interesting proposal, the lookback time evolution seems to match the observational values of the current Hubble parameter $H_0$ at any $z$. In this comment, we discuss that using a lookback time approach function $H_{0}^{(z)}$, does not address the $H_0$ tension issue completely. It has been studied that the growing tension among early-time and local measurements of $H_0$ are possible concealed sources of systematic error in observations or modifications (or extensions) to the standard $\Lambda$CDM model. Furthermore, we show that the age of the Universe is sensitive to both $\Omega_m$ and $H_0$ in flat $\Lambda$CDM-like cosmological models.