I think children should get the vaccines ASAP provided the vaccine is proven safe as missing a year of school is going to have profound impact on their life and society. Many students from marginalized society, especially from poor countries might never go to school again as they have been employed by their parents for meager sum.
But I think definition of who's 'vulnerable' is what going to be contentious, apart from obvious front-line workers and elderly whom would you decide are vulnerable? Immunity compromised individuals? I'm myself house ridden for over 2 years now due to spine surgery and so likely immunity compromised but there's no way that could be informed to the Govt. I just hope my elderly parents get their vaccine.