Really? I'm speaking from a US perspective, but my opinion is the communication out of the CDC has too much nuance and is too concerned about being scientifically accurate. They forget they're speaking to a largely scientifically illiterate crowd, and that crowd sees the constant back-and-forth not as scientific progress but as a reason not to trust the institution. Never mind that it's often delivered with a tone of condescension people have come to despise from their institutions, and some of their policy recommendations are... debatable to say the least (recommending mass testing for high school sports/band/choir, for a recent example).
Honestly I only trust the CDC because I have the knowledge and capacity to verify what they say and ignore the bullshit. A lot of people don't have that. And there is bullshit to filter.
The message to the public, assuming the CDC is interested in actually convincing people, needs a simple path forward individuals can take to get said individuals something they want, even if it taps into a selfish motivation and isn't 1000% technically optimal. (i.e. Get vaccinated and the mask requirements go away). And it should be repeated in every statement, regardless of new data. It should have been consistent for the past 2 years. It should have a catchy slogan. It should be on fucking billboards. People would still bitch and grumble, and some would never be convinced. But we'd probably have more people vaccinated if that approach had been taken. Instead we confused people and handed ammo to the anti-vaxxers by the truckload, relying on peoples' better natures and assuming a higher average level of education than actually exists in the American populace.
In short the CDC should optimize for leadership and "good enough" solutions, not strict scientific accuracy and trying to save each and every life in their public statements. Publish the hard science/raw data in more obscure releases that only scientists will care about. And they need a better front person than Fauci. Fauci just radiates highly-credentialed-beltway-insider arrogance however nice he tries to sound and however right he may be.
Of course you could argue such a role should be the place of the executive, and the CDC was trying to fill the gap left by a largely absent Trump administration, and by the time the Biden admin took over Fauci's position as front-man/leadership was already too solidified. Maybe so, but the CDC and public institutions in general have failed the task of public leadership, although thankfully have had success in logistics/vaccine development.