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Do you know the reasoning behind prioritising the young? They are the most social age group, so if the idea is to achieve general immunity, it makes sense.
I'm not certain of the federal government's reasoning, but if I had to guess or give my own reasoning, I think it's exactly what you said.
I think that more people aged 30-65 are able to limit their exposure by working from home, whereas we want to keep children in schools and maintain their interactions for healthy social development. Unfortunately we have seen repeatedly that schools and universities act as amplification points for the virus, and although children are at low (but nonzero) risk of severe illness, they can still transmit the virus to their parents who may be at higher risk. So by immunizing children first, it may allow schools and universities to function safely in person while also reducing risk to parents and teachers, and thus help protect two populations at once.