"The rankings did not account for things like population density, the close quarters in urban households or use of public transportation, all of which play a role in virus transmission."
This goes well beyond the critique if any CDC study.
They neglected to correct for any of the complicating factors. As a result, you can't tell the difference between the effect of lockdown, the effect of population density, and any other effect that correlates with being a major urban center.
This makes the study less than useless, and you know it.