If you can correct the agent to go where you want, it already wanted to go where you want. If the agent is strictly corrigible to terminal state A, then A was already optimal for it.
If the reward function has a single optimal terminal state, there isn’t any new information being added by πcorrect. But we want corrigibility to let us reflect more on our values over time and what we want the AI to do!
If the reward function has multiple optimal terminal states, then corrigibility again becomes meaningful. But now we have to perfectly balance the reward among multiple options (representing the breadth of our normative uncertainty), which seems unnatural.
Edited to add: