CDC might be wrong here but they will never admit. Never.
They (we) did. A list containing children under 12 who got vaccinated is at the center of a data breach this very week.
There was also an uptick in deaths among young school-age children, which was somewhat 'offset' by lower deaths in the 12+ age-ranges. Vaccinating children doesn't do nothing, but with a small effect focusing on small at risk groups might be wise.
Things have been substantially better for my wife and I since we started Paxlovid. Our seven year old is feeling fine, and our three year old who is disabled and tends to get sick fairly often has a fever and slept for a day straight and had the world's worst diarrhea. Her doctor (who almost exclusively sees disabled kids like her) seems completely unconcerned about it and said to just treat it like any other illness, push fluids and give her Tylenol and Ibuprofen alternately to keep her fever down.