The coronavirus is more severe for children than the Flu, but even setting aside that there's reasons to vaccinate a subpopulation besides individual benefit.
We routinely vaccinate kids against Flu mainly because they are a significant source of community transmission, primarily via schools. Toddlers actually have higher Flu vaccination rates than the elderly.
This is a vaccine that has lower effectiveness than the coronavirus vaccine and has lower ability to stop infection/transmission. But the net community benefit is significant.
As we are seeing now and likely will see in the endemic phase of SARS-COV-2, children have the highest rates of infection and are significant sources of transmission in this Delta wave. They efficiently transmit to adults in households. Lacking the immunity of previously infected or vaccinated adults they'll likely sustain community spread of the coronavirus in the future.
At the individual level, there's a net benefit to vaccinating children of all eligible ages, but we shouldn't overlook community benefits. There's quite a few vaccine-preventable diseases we primarily vaccinate kids due to the community benefits. SARS-COV-2 should be no different.