It is not clear why exactly Bristow would have wanted to risk everything and ask someone to investigate all over again, but here is my guess: It is true that his family was wealthy, but John Bristow himself was a lawyer in a law firm and could not afford to pay Onifade's blackmails. I think he thought his plans were perfect and flawless since the police did not even find out it was him. We found out in the book that Bristow chose strike because he had researched about his mother who had died while some people, including Strike, thought he was murdered. Bristow thought Strike had a blind spot for these types of crimes and would not be able to solve them because he would remember his mother. He paid strike to prove that again do that no matter
