This is less clear-cut than it seems because nearly everyone that's highest risk is retired and doesn't really need to leave the house. Is it better to tell a dozen pensioners that leave the house once a week for grocies to stay home so younger people can get vaccinated and go back to work? Possibly, depending on who you're asking.

Younger people are far more mobile and so contribute greatly to the spread of the virus. The old and sick don't go out much so aren't the ones spreading the virus.

Is it more important to stop the spread as quickly as possible or directly vaccine the more vulnerable? It's hard to know, and it probably depends on how much vaccine you have. Countries like the US with lots of vaccine may be better off vaccinating the most mobile members of society first to drop total infections ASAP. Countries with less are better off focusing on the vulnerable because they're a long way from herd immunity.

If you have enough vaccine supply you will minimize deaths by eliminating transmission quickest which implies vaccinating the most exposed, not the most vulnerable.