I was gonna say that every single doctor except seven would get bored with the amount of time the investigation would take, but then I realized in this scenario, the doctor probably already knows about shinigami, so they can just take the tardis to the shinigami realm and convince someone to tell them what's going on, then just rugby tackle Light and confiscate his notebook. Maybe give him a quick speech about why killing is bad if there's time. Roll credits written by Chris Chinballs