The US is apparently a big outlier in the number of reported children's deaths (5 per million) compared to other developed countries. There are also other confounding factors such as under/over reporting of symptoms and side effects. See here for a review: https://onlinelibrary.wiley.com/doi/full/10.1111/eci.13678
the mortality in kids seems to be orders of magnitude smaller than the seasonal flu:
> as of May 2021, data from 79 countries accounting for 2.7 million COVID-19 deaths (69% of all documented global COVID-19 deaths) show that over 8700 (0.3%) of these deaths are in children and adolescents under 20 years of age (40% in children 0–9 years old and 60% in adolescents 10–19 years old). For illustrative comparative purposes, estimated annual fatalities for seasonal influenza preceding the COVID-19 pandemic included 9243 to 105,690 deaths of children younger than 5 years
The comparison to make isn't to the risk of dying from everything else, it's to the risk from vaccination.
Which there isn't really anything published for young children yet, but for age groups where use of a vaccine has been approved in the US (12+ more or less), the risk of severe side effects from vaccination is lower than the risk of severe illness.
Annualized, that's about 25 per 100,000. So COVID won't be the leading cause of death, but it's high enough to be classified as a major source of child fatalities.
For something easily preventable once the vaccine is available.
You're right, atypical influenza is also risky. I know people who have died from it, and have two close friends that have had their life ruined by side effects from H1N1. (Guillaume Barre syndrome and Chronic Fatigue). I wouldn't wish either of those on my worst enemies.
Some risks in life you have to accept, but ones that are trivially avoidable?
Shutting down schools to prevent children from getting COVID has too many side effects given the risk level, but the vaccine has such a low cost and so few side effects.
Except it would not be far fetched to think that child cases are vastly under-reported. My wife and I both tested positive and my three children showed mild symptoms. I saw no reason to go through the hassle of getting them tested when it was clear what it was.