I could have a very poor understanding of how vaccines work, so someone feel free to correct me, but even once people are vaccinated can they still "get" covid and test positive. Having a vaccine doesn't mean the virus can't enter your body, it just means that you can fight it when it does.
The current policy requires a team to go on pause even when someone who tests positive is asymptomatic.
Again I might be wrong about how vaccination works, but unless they change that policy and stop testing once the players are vaccinated (unlikely) then it doesn't make sense to prioritize them since they can still carry & transmit the virus, leading to asymptomatic positive tests and thus more shutdowns.