One other point on why we want to vaccinate children: there is no way we can get to herd immunity without including kids. herd immunity is when there are so many people vaccinated that probability dictates that the virus cannot spread and it eventually dies out. for COVID, estimates are we need ~70% minimum.
Herd immunity is what we will use to protect those who either refuse the vaccine, those who cannot take it for medical/religious reasons, or for the very small population for whom it will not work (i.e. no vaccine is 100% effective).
A quick google search shows
22% of US population is under 18 - to get to 70% of the population, we would need 90% of everyone else. Because anti-vaxxers exist, I'm not sure that's possible.