From the way I see it, using a new save only adds a few seconds to a run. Think about it; it's well established that you end a run for this game right after the final fight with Sasuke, so the extra cutscenes you need to skip wouldn't be added to your total time, regardless if you used a new save or not. I would also say that constantly having to refresh a new save file constantly, especially if you need to restart a run in a timely fashion, isn't worth it. Doing well in the Hashirama vs Madara fight is crucial to get a good starting time, so getting it perfect would require multiple restarts, which would be a hassle if you need to constantly make a brand new save file.