One way to understand the history of detective fiction is to weigh out the changing balance between character-building and the central plot.
The Victorian ancestors of "detective fiction" proper were much richer in character than in plot. Consider The Moonstone, whose pleasure derives not so much from a stolen diamond as the round robin narrative eccentricity. The novel shows us not crime in a bare form, as golden age crime novels do (though always dressed with an inconsequential motive as though to better accentuate the ingeniousness of the act itself), but rather a relationship between character and crime. The early and mid 20th century saw a great many stripped down crime novels. Conan Doyle, the four Queens of Crime, Erle Stanley Gardner, Rex Stout, most pulp writers, etc. - all of them reduced characters to a few distinct qualities. Sometimes this sketch captures the reader in a jovially Dickensian way (e.g., Doyle or Stout) and sometimes its obvious staginess had a curious distancing effect (e.g., Poirot or Perry Mason). In all cases, however, the emphasis was on static characters, whose personalities are understood to exist separately from the experiences they undergo in the course of the novel.
There were a lot of important character heavy books from the mid-century that foreshadowed a shift in balance in favor of character. Mystery is clearly a secondary element in Chandler's work (hence the famously indeterminate murder of the chauffeur). There are two central elements. The first is dialogue and the second is character. This is not to say that the mystery plot is in the margins. It remains front and center as a pretext for a paranoid grand tour of the interconnected corruption at different levels of society. Mass market writers in the sixties (Day Keene, Bruno Fischer, etc.) tend to offer a stripped-down version of the paranoid tour. If anything the view of society is even more anatomical, as stereotyped characters of all classes and professions are shown to be working for corrupt interests.
This societal anatomy is formalized and delimited in a couple places. The first is the Cold War novel, where the characters are still in disguise, in that they have a cover rather than openly working for corruption. However, rather than a society of anarchically grasping people as in classic roman noir, the source of the corruption has been elegantly pared down to bad ideology. Then there is the success of the Mafia novel, where crime is similarly centralized (and therefore segregated from standard everyday American society) but cover becomes less important. These are still social anatomies, but the social rot is heavily circumscribed, unlike Chandler, where one can walk into any house and find a murderer.
In all paranoid tour novels detection loses its centrality. The revelation is not the reconstruction of the true story of the crime by the detective, but that society itself is complicit. The crime is a symptom, not the illness itself.
The Hoke Moseley series is a take on the paranoid tour, but also a parody of that paranoid mode. Society is pretty much irredeemable, yes, but rather than an anatomy of the social structure, one finds that society is hopelessly fragmented. There are not conspiracies, not even destructive ideologies, just greed, bad luck, and stupidity. Moseley's haplessness is correlative. The mystery novel has always been about social structures. The detective has to look into the crowd and judge. In Miami, where crime is so anonymous and society is entirely incoherent, the task itself is absurd, and can therefore only be solved through dumb chance.
What most people find "weird" about New Hope for the Dead is that it has no center. There is little direction, little crime, little detection. We spend a lot of time just hanging out with Moseley. The central plot is about his difficulty finding an affordable new rental within Miami city limits. Willeford explodes the standard paranoid novel tactic of using a single crime to reveal a web of evil, showing instead disconnected institutional, cultural, and financial factors that are stumbling blocks. Crimes aren't united by collusion, but by life in Miami. It is not a novel of social criticism, to be sure. Willeford's reaction is bemusement, not concern. Miami is a human zoo where social controls are so broken that our native anarchy reigns.
To put this into historical perspective once more, the classic detective story is about the conquest over disorder by society, an effective use of social controls. The paranoid detective story is about the tragically (if excitingly) hopeless pervasiveness of corruption. From one perspective, this is a breakdown of social controls, but what is always revealed is that there is a parallel society of crime operating under the cover of regular society. Willeford, more existential, sees that the breakdown has really destroyed the concept of society. There are conditions, and there are people. Willeford sees this with a kind of comic libertarianism. This diminished sense of belonging is frustrating, tiresome, but above all funny. Your classic detective helps render society coherent. Moseley, more dizzy, registers the incoherence and absurdity of Miami, an incoherence that seems part and parcel with the city's particular human freedom.