The CDC does not have authority to regulate housing:
A federal judge on Wednesday threw out a national eviction moratorium, saying the Covid-19 pandemic-relief measure exceeded the powers of the Centers for Disease Control and Prevention.
Source: National Eviction Moratorium Thrown Out by Federal Judge – WSJ
The CDC had no legal jurisdiction over housing contracts any more than the say the SEC could regulate health care. An eviction moratorium was a the wrong way to solve the problem they were seeking to solve.
[…] May, 2021, a Federal Court rules against the CDC’s moratorium eviction, saying the CDC, under the Public Health Act, lacks jurisdiction to regulated housing and housing […]