I've gone over the numbers the BBC keeps pushing a while back when another article was posted on HN so I'm not going to repeat myself, but in summary the problem is that these numbers are given as "deaths per population" without taking the number of infections into account. There's also no evidence that children are at a lower risk of developing Long Covid.
Note that these same sources also espouse that children are safe because of their lower infection risk but then go and compare the mortality rate to the entire population to come up with grandiose claims. When looking at the actual official UK numbers (i.e. comparing deaths after a confirmed infection to confirmed infections) child mortality is indeed significantly lower but only by a factor of 10 compared to adults. This paints a far grimmer picture than all this talk about there being a multiple orders of magnitude difference.
It's also worth pointing out that the vaccine supply is limited, so the question of whether children should be vaccinated is one of prioritization. If children already have a low likelihood of infection and have better outcomes than the average adult, it makes more sense to use that vaccine on an adult than a child.
German media also suggests the decision for the German vaccination authority to not recommend a third round of vaccinations at the moment is similarly driven by the idea that it's more important to make sure everyone has some level of immunization than that some people have a very high level of immunization: the goal is to control spread, not to protect individuals. Note that the German authority has greenlit vaccinations for 12+ year olds, so their risk evaluation seems to consider the likelihood of children spreading the virus or potentially developing chronic conditions in the future to be significant enough. Of course you can't compare these risks directly due to differences e.g. in the school systems and pandemic-related accommodations.