An absolute handful of children have been (possibly; causality unclear) sickened by the COVID-19 vaccine.

About 1,000 children have died of COVID-19 in the US (https://data.cdc.gov/NCHS/Provisional-COVID-19-Deaths-Focus-...).

The exact details of why the virus hits children less hard are unclear; one theory is that the primary cause of lung-failure death in adults is a cytokine storm (i.e. the immune system reacting to the virus by attacking too many healthy cells at a rate the body can't repair), and a younger, more naive immune system is less likely to have picked up whatever environmentally-primed triggers COVID-19 aggravates to kick off a cytokine storm.

... but sadly, "less likely" isn't "didn't happen," and if that causality is correct, some thousand unlucky kids have gotten snake-eyes on the immune dice and died of a disease that we can now vaccinate for. That's an order of magnitude more children than the number we even suspect of being sickened by the vaccine.

We should vaccinate those who haven't been vaccinated because the risk balance is pretty clear at this point from the gross numbers we have on under-18 vaccination already.

from your source:

> COVID-19 deaths are those with confirmed or presumed COVID-19

i.e. 1000 children have died with COVID, not of COVID. Big difference.