To me it boils down to what is to be measured here. With logprobs we can measure both correctness and not attempted i.e. if LLM is guessing the response.
Similar to exams where both the progress to the solution and the final outcome/value of the calculations are part of the grade.
To have the cake and eat it too for chain-of-thought reasoning, one way is to ask for a "final answer" so the final response token logprobs can be evaluated https://chatgpt.com/share/67239d92-b24c-800a-af8c-40da7be1f5...
Another trick is using JSON mode to keep intermediate results and final response separate, so each can be graded accordingly.