The paper by Hao Wang and Yun-Song Piao examines the impact of recent DESI BAO data on the state equation of dark energy (DE) in cosmologies that resolve the Hubble tension. The DESI collaboration reported a $\gtrsim 3\sigma$ evidence for evolving DE against the cosmological constant (CC), challenging the standard $\Lambda$CDM model. Using DESI BAO measurements combined with Planck CMB and Pantheon Plus data, the authors perform a Monte Carlo Markov Chain (MCMC) analysis for the $w_0$-$w_a$ CDM model, considering pre-recombination resolutions of the Hubble tension. They find that while $w_0 > -1$ and $w_a < 0$ are still preferred, the CC remains consistent with the data within $2\sigma$. The best-fit Hubble constant $H_0$ is higher than those without DESI BAO data but without exacerbating the $S_8$ tension. The results suggest that the preference for evolving DE may be suppressed by the resolution of the Hubble tension, indicating that the claim of ruling out the CC needs to be cautious, considering both recent observational data and cosmological tensions. The study highlights the importance of understanding the nature of DE and the role of early dark energy (EDE) models in resolving the Hubble tension.The paper by Hao Wang and Yun-Song Piao examines the impact of recent DESI BAO data on the state equation of dark energy (DE) in cosmologies that resolve the Hubble tension. The DESI collaboration reported a $\gtrsim 3\sigma$ evidence for evolving DE against the cosmological constant (CC), challenging the standard $\Lambda$CDM model. Using DESI BAO measurements combined with Planck CMB and Pantheon Plus data, the authors perform a Monte Carlo Markov Chain (MCMC) analysis for the $w_0$-$w_a$ CDM model, considering pre-recombination resolutions of the Hubble tension. They find that while $w_0 > -1$ and $w_a < 0$ are still preferred, the CC remains consistent with the data within $2\sigma$. The best-fit Hubble constant $H_0$ is higher than those without DESI BAO data but without exacerbating the $S_8$ tension. The results suggest that the preference for evolving DE may be suppressed by the resolution of the Hubble tension, indicating that the claim of ruling out the CC needs to be cautious, considering both recent observational data and cosmological tensions. The study highlights the importance of understanding the nature of DE and the role of early dark energy (EDE) models in resolving the Hubble tension.