In a free market, vaccines would be sold to the highest bidder. The government could buy too, but you wouldn’t be forbidden from buying them yourself, and companies and schools would not be forbidden from buying them for their employees. Businesses would likely pay top dollar to vaccinate crucial employees who are off the job due to the pandemic. And only businesses know just which employees are crucial to the economy, and which can wait.
Government rationing gives power to public officials. It does not necessarily lead to superior moral outcomes. So far, the main accomplishment has been to slow the rollout.