The simplest and the shortest answer to that will be that as the complete roles will be revealed, the cop / lie detector / tracker get the necessary freedom to play the game and that certainly helps in getting (rather revealing) useful information soon.
Vedarshi needs to role-claim here.
They get the freedom as they know whether the doctor is dead or alive. And yes, I'm heavily banking on the night roles, have never really been a huge fan of the concept of starting the game with a day phase.