One of the more interesting arguments about this that I have read is in Jeffrey Herf's 1984 book Reactionary Modernism. He frames the Nazi approach to nationalism as such (35):

The core juxtaposition of [the Nazis'] nationalism was that of Kultur and Zivilisation. On one side stood the Volk as a community of blood, race, and cultural tradition. On the other side was the menace of Amerikanismus, liberalism, commerce, materialism, parliament and political parties, and the Weimar Republic. Nationalism served as a secular religion that promised an alternative to a world suffering from an excess of capitalist and communist rationalization. German nationalists elevated Germany's geographical position between East and West into a cultural-political identity as well. The Kulturnation would escape the dilemmas of an increasingly soulless modernity.

In other words, it wasn't just about elevation of a single German national identity, it was about defining that identity in a very specific way, one which led to a rejection of Enlightenment values, certain types of non-German Western influences (American, French, British), and (non-coincidentally) Jews (who were associated exclusively with Zivilisation in the pejorative sense). It was a way to sub-divide German people, German politics, and German traditions in a very particular way, in a way that was much more specific than the general pan-Germanic nationalism that had been used to unify the country under Bismark.

I have found Herf's analysis a nice way to explain many of the peculiar aspects of the Nazi ideology (e.g. how they can simultaneously embrace agrarianism but also embrace certain forms of very high technology, like rocketry and romantic notions of interstellar travel), though there is something of a "too clever by half" aspect to it (it makes ideology into something that is just a little too rational for my tastes). But as a retrospective analyst tool for making sense of the specifics of Volkisch nationalism and what it contrasted itself with, it makes a useful starting point and it has a nice provocative argument.

the somewhat mythical idea that the Germans as an ethnically exclusive people, and a nostalgic emphasis on agrarianism

The initial wave of German nationalism was very much a reaction to the plain ol' regular French counterpart. The first German nationalist organisation, the Jena Burschenschaft was formed by student-veterans who fought against Napoleon and now appealed for a united Germany that still was pronouncedly conservative. The current flag of Germany is indebted to that very organisation.

Eventually Burschenschaften would appear in other German towns and since there was no German state to make up your classical nation of citizen-nationals they'd spend a lot of time pinning down being German to particular manners or dress. In 1817 the Burschenschaften assembled in Wartburg (where Martin Luther wrote his German bible) to burn books deemed too foreign and too liberal, including the Code Napoleon. In 1819, after the dramatist August von Kotzebue got assassinated by a Burschenschafter these organisations were banned but continued to thrive in the underground of all the university towns that spoke German.

In 1820 the secret Burschenschaft congress in Dresden excluded Jews as potential members. The poet Heinrich Heine was evicted from the Göttingen Burschenschaft around that very time. In his «Ludwig Börne: a memorial», of 1840, he describes them like that:

Despite their ignorance, the so-called Old Germans had borrowed from German “larnedness” a certain pedantry that was as repulsive as it was ridiculous. With what petty finickiness and pickiness they discussed the distinguishing marks of German nationality! Where does the Teuton begin? Where does he end? May a German smoke tobacco? No, claimed the majority. May a German wear gloves? Yes, but only of buffalo hide. (The dirty Massmann wanted to be on the safe side and did not wear any.) But drinking beer is permitted to a German, and he should do it as a genuine son of Germania, for Tacitus speaks quite precisely of German cerevisia. In the beer cellar at Göttingen I used to have to admire the thoroughness with which my Old German friends created their proscription lists for the day when they would come to power. Whoever descended in the seventh generation from a Frenchman, Jew, or Slav was to be condemned to exile. Whoever had written the least thing against, say, Jahn or any Old German absurdities could prepare himself for death, specifically death by the ax, not the guillotine, even though this was originally a German invention and already known in the Middle Ages under the name of the “Welsche Falle.”

(translated by Jeffrey L. Sammons. See the German text here)

The Hambacher Fest of 1832 was the plain ol' regular (liberal) nationalist counterpart to the Wartburg Fest. Eventually that strain got the upper hand and once Germany became a national state there appeared a need to distinguish publications that still clung to the essentialist folkish tradition tipped off by the Burschenschaften.