It does reduce transmission. In kids it massively reduces infection rates (and if you don't catch it, you can't pass it on), and it reduces severity (and transmission) in those unlucky enough to catch it. That also reduces the number of school days etc they miss, as well as any spin-offs in terms of protecting classmates and other people.
The "dangerous to kids" thing is relative. Covid is more dangerous to kids (in terms of deaths/hospitalisations) than the covid vaccine. There's also still a lot of debate about what proportion of under 18s who do catch covid have lasting (one month plus) after-effects, but again those long covid issues are far more common than vaccine after effects.
In the UK, the MHRA/JCVI have gone for a slow and cautious approach but still recommended a single dose for 12-15s and a double dose for 16+.