While I agree that the ending could have been better, I think it is not as strange as
@Cloneable suggests.
No, they could not legally just pull out a gun and kill him. That is not how any modern justice system works. It may be frustrating, but there are valid reasons for having it this way. There are plenty of revenge stories that ignore law. This was just not one of them.
And, it is not clear Takeda was cured per se. It just seems the cancer had not gotten worse yet. In real life there are instances of miraculous cures. There are even more instances where a patient’s state of mind and/or emotions played a role in recovery or worsening. This is plausible.
As for a motive: Nakamura raped and killed Sawako. The motive was he wanted to have sex with her and then needed to cover up his crime. It’s self-explanatory.
The main point I agree on with
@Cloneable is the issue of the radio. That was a bit of a stretch. It is kind of an odd thing for some average person to know what the rule of the statute of limitations is (that it counts down from confirmed day of death). Either Sawako is being portrayed as an inexplicable genius or else perhaps she recorded the numbers for other reasons (just to try to keep sane?). Could definitely have been better justified.
Still, really good story.