All adults won't take it though, will they? I guess it's easier for Gov to find ways to sanction parents for not allowing their kid to have the vax than it is to sanction an adult for refusing the vax for themself.

The main reason they will give is the mutation issue. Kids can still catch and spread the virus to vaccinated adults, even if those vaccinated adults don't get the severe symptoms due to having had the vax. The more the virus spreads then there is that increased risk of a terrible mutation. It's been said that the preliminary vax data shows there is a reduction in transmission. Whether that is what actually happens outside of a trial is another matter. (Don't confuse it with immunity to infection itself because that immunity doesn't exist with this virus).

So the Gov will argue that the kids need to be vaxxed to help get the R number as near to 1, or below 1, as possible in the community, in order to reduce the chances of troubling new variants popping up.