In supervised learning, the data that we have is real world data, and we want our model to mimic that input-output mapping as much as possible. For example, if we have MRIs of patients and we want to detect whether that patient has a cancer or not, then ofcourse we would want our model to predict every single patient correctly.
Now, come in the Reinforcement Learning domain. You have an agent, it acts in an environment, gets reward and another state, and sometime later the episode ends. The data on which the policy function neural network will be trained on, will the the data generated by the agent. And using the Monte Carlo Tree Search, the agent would pick the better action which he thinks is better. Now, the actions that the agent made at the corresponding states in one learning run, will become a training dataset for the other learning run. So, in the second learning run, if the agent is mimicing it's actions completely, then, well, it's not learning at all. It's just selecting the same actions over and over again, which kills the purpose of Reinforcement Learning.
Reward is the correct metric for Reinforcement Learning model assessment.