In which case we would have had a wave of evictions and a spike in homelessness during the most difficult phase of the pandemic -- when we had no vaccines, limited testing capacity, and hospitals that were way over capacity with COVID patients. That would have left many more people dead and greatly reduced compliance with social distancing rules as desperate people (facing eviction or already evicted) skirted the rules in an attempt to make enough money to cover their rent. It would also have given people an easy excuse for dismissing the CDC's guidance in general, since the CDC would have been making a completely unreasonable demand ("stay home" is unreasonable if you need to leave your home to show up at work so you have enough money to make rent).

The CDC does not have the ability to pay everyone's rent. If we could have relied on state governments or Congress to bail out rent for people who were unable to make rent otherwise, maybe the moratorium would not have been necessary. Unfortunately, that is not even remotely something we can rely on -- we have spent over a year arguing about whether the "relief" checks, which would not even cover rent in many cities, are too generous.

Emergency powers are not a problem -- in an emergency there is no time for political parties to work out some kind of deal or for judges to review facts / legal arguments, and we allow certain government agencies to take emergency actions in such situations. Look at how long it took for the courts to overrule the CDC; if that is how long it took to react to emergencies we would be at the mercy of every fire, disease outbreak, hurricane, etc. The only relevant question to protecting democracy is, "How long should an emergency order remain in effect before the legislature or judiciary gets involved?"