The chase of the truth, or a least the semblance of truth, thrills them.
Money is only a pretense for their true motive for taking the case.
Desire is the real driving force behind detectives' actions, and the desire leads to lust, obsession, and fetishizing. The chase of the case then satisfies them far more than, and thereby replacing their need for, sex. Philip Marlowe, in Raymond Chandler's The Long Goodbye, has a fetish for mysteries, sticking to a case even when no-one clearly employs him. His need for the mystery exceeds his need for employment. For detectives, the pursuit of the victim yields more pleasure than its capture.