But would it? California had mask mandates. Florida and Texas did not. And if you look at the COVID cases during the Omicron wave, none of these states flattened the curve. California's cases went straight up and then straight down. Same with other large states without mandates. There was no flattening the curve regardless of masking policy. Also, there are negative impacts to mandates and mitigations to other elements aspects of life that must be weighted against their benefits.
Optimally everyone in the US that is eligible would get vaccinated, but that ship has sailed. Those that have rejected vaccination will not be moved by government programs and pressure. They have dug in. I am a big supporter of vaccinating adults, especially those that are most vulnerable to hospitalization and death. Unfortunately, while very effective against serious illness and death, vaccination has not proven to be very effective against Omnicron infection. So, the benefits of vaccinating young people (very unlikely to get severely ill) and mask mandates in schools to slow the spread seems substantially less with Omicron.
I am not sure how much better of a place we need to be in before there is a change of policy. Estimates are that 90% of the population now have some form of immunity (natural/vaccinated). We have treatments. We have testing. Cases are plummeting. Hospitalization are plummeting too, but the data is questionable at best, since there is no distinction between those hospitalized "with" vs "because" of COVID.
Finally, we have a public that has grown cynical of government programs and officials that have lost credibility, such as: Hypocritical politicians that don't follow the guidance they put in place for others or, "Noble lies" told by Health care officials to influence behavior. Experts and officials have burned all of their chips. The public is done.
Time to stop using a broad ax approach and focus mitigations and prevention on those most vulnerable. 75% of deaths are over 65. A huge percentage of deaths are obese. How about a medical surveillance program for the 90% that have the highest likelihood of serious illness and death? At most universities, College kids are required to be vaccinated and tested weekly. These are the people least likely to get severely sick. Meanwhile, there are no such medial survellience programs for the most vulnerable. Insane.