At the end, Harper is hellbent on tracking down Julie Harris who hot-wired his car resulting in a fatal car chase. Why was it necessary for Harper to go to such extreme measures to risk injury to all parties when he(1) had the key to the storage locker with the money and (2) knew where the kidnapped man, Samson,was being held.
Earlier in the movie he had shown signs of becoming obsessed with solving the case, or cracking the case and laying it wide open, as he said to Graves, the attorney. I assume he meant he was not just going to find Sampson, but find all the kidnappers involved, and bring them to justice.
Harper had discovered that Betty Fraley was not only involved in the kidnapping plot, but that she had also shot and killed her brother so as to run off with the ransom money. Harper was chasing her down because he wanted her to stand trial for those offenses. And who knows, maybe he also wanted his Porsche back?
(Mrs. Sampson only hired Harper to find her missing husband. Hey, she got the bonus plan!)
I think Harper was no Mike Hammer. Far from it, much more laid back. Look at the way Harper treated Robert Wagner and reacted when he was shot even though Wagner had a gun on Harper. At the very end, Newman had an "aw shucks" attitude in bringing his pal to justice. Just the opposite of obsessed. The answer lies elsewhere.
My take on it is that he had no personal use for the junkie/brother killer (Fraley). So he had no qualms about hauling her in to face justice. As to the attorney, he almost busted him, too, except for the fact that the attorney shrewdly convinced Harper that he was not only Harper's best friend, but his only friend. So yeah, he relented and had that ‘aw shucks’ moment in the very end, but that doesn't mean he wasn't previously obsessed with bringing them all in to face justice.
In the book we hear from a Highway Patrolman who chased her down for speeding and she lost control and crashed. One of the things that made Archer suspicious of Albert was that she was alone in the car - i.e. no 'fourth kidnapper'. I think the real answer is 'he didn't need to go to such extreme measures'. I guess Hollywood needed a car chase and needed Newman to appear to show off his driving skills.
It's funny the variety of acting styles in one film from Julie's intense method acting on the one hand to Wagner being RJ and Pamela Tiffin's posing on the other. In between, there's Newman channeling Bogart taking it more seriously than say, Mrs. Bogart's mocking derision.