It's a scientific question as to whether a specific limit on freedom (of movement, of contact, etc.) is effective.
But it's a general approximation that greater freedoms mean higher mortality rates during lethal pandemics. And vice versus.
What level of mortality we're prepared to accept, and what level of limitations on freedom, is a political question in a democracy.
That's the eternal question. Not just for disease control, but for everything.
> What are the criteria for determining necessity?
In a democracy, ultimately: elections.
Ahh, I see where the confusion is. They actually have authority to issue legally binding orders.
"To help prevent the spread of COVID-19 and help our country cope during the pandemic, CDC has occasionally issued legally binding orders and regulations."
https://www.cdc.gov/coronavirus/2019-ncov/cdcresponse/laws-r...
Not all such orders are listed on that page. For example, "CDC Director Dr. Rochelle Walensky today signed an order determining the evictions of tenants for failure to make rent or housing payments could be detrimental to public health control measures".
https://www.cdc.gov/media/releases/2021/s0803-cdc-eviction-o...
The CDC's mission is fundamentally the same as the mission of the Chinese disease control agency. The difference is how that mission is balanced against people's freedom to live their lives.
Please don't misunderstand; that doesn't mean that I oppose everything they do. Everything they do limits freedom, but sometimes that is necessary.