Why did Hitler not claim the German-majority areas of Schleswig?

As historian Mark Mazower put it: The Nazis always fabulated about thousand years and were often incapable of thinking 5 minutes ahead. That means that there were many plans, often grandiose in nature, in scope of time and space, that were seldomly thought through or followed through and much of the time of quite an ad hoc nature. Not the least because Hitler was far less influential as commonly thought and the Nazi system of politics and decision making in fact quite chaotic. Many cooks added their salt into the broth.

But in this case I would like to cite Semaphore's condensed common sense first:

The area involved is not just tiny and contains nothing historically significant, but also had very few Germans, isolated pockets notwithstanding. Compare with Memel, Danzig, and the 3 million in Czechoslovakia its easy to see why it gets overlooked. Hitler didn't get around to Eastern Belgium (detached by Versailles) before the war either.

That correctly identifies the small gains available by reconverting Sønderjylland back into Nordschleswig. Further we have to keep in mind that the post-Versailles partition of a medieval duchy may not have been ideal or even ideally possible according to language or ethnicity based reasoning. Thoroughly mixed up people (and less than 150.000 voters in Nordschleswig in 1920) between rural and urban spaces with little practical significance regarding positive changes to the war effort.

On the contrary, we might conclude that the Nazi sympathy for their nordic racial comrades was not only conducive to much milder treatment in general but also a prerequisite for the Nazi's hope of genuine collaboration during the war and after that. We do not need to resort to the conspiratorial revisionist historiography of claiming a general pact between Danes and Germans, but the occupation operation was indeed quit uneventful and low in losses of human life and thereafter Denmark enjoyed a very special treatment until 1942, not in the least because of German wishful thinking of joining genetic forces to better breed the master race to fight the racial war.

Gaining little but angering potential allies doesn't seem like a good plan. After the guns were so successful it was time to ensure the butter was kept coming. That might be the main reason for German elites envisioning at least since World War One¹ their Mitteleuropa: preforming the European Union as an economic block co-opting racially compatible nations, expropriate racially inferior nations and exterminating racially unworthy enemies. Hitler's overall geostrategy should be read with a healthy dose of salt after re-reading the first paragraph of this answer. But the ever popping up of Mitteleuropa plans (another example by Ribbentrop) are indeed the general guideline to consider here.

Mark Mazower: "Hitler's Empire. Nazi Rule in Occupied Europe" Allen Lane: London, New York, 2008:
On 9 April, Denmark became the first country to capitulate. The invasion was over in a few hours, before the Danes had even had time co declare war: resistance was patently futile. As a result, compared with Poland, they were handled with such a degree of moderation by the Germans chat it is difficult to imagine the same state was responsible for dealing with both. In the case of Poland the Nazis trampled on international law and erased the country from the map, whereas the Danes negotiated the mildest form of German oversight anywhere in Europe. The country remained formally independent, and King Chris­tian stayed on his throne: Copenhagen continued to be the political centre of Danish life throughout the war, and those politicians who fled abroad found themselves marginalized. The parliament continued co function, and there were even surprisingly free elections in 1943 – we know this by virtue of the fact that the Danish Nazi Party won barely 2 per cent of the vote and was trounced by the old prewar parties. German wishes were transmitted through the former ambassador, Cecil von Renthe-Fink, who became Reich plenipotentiary, supervising Danish affairs with a tiny staff and a Iighr touch. The country's territorial in­tegrity was guaranteed, and the small German minority was firmly told not to make trouble.

Renthe-Fink emphasized the importance of keeping the 'outward appearance' of independence in order to weaken opposition to the Germans elsewhere. Keen to move on to Norway, the Fuhrer agreed: in Denmark there was to be no civilian administration, and even the army played only a modest role. It was 'political window-dressing' perhaps – as one Nazi official termed it later on – but first impressions were important at a time when the Germans did not know how the invasions of Norway and the Low Countries would turn out. Such an arrangement also promised to guarantee what Germany really needed from the Danes – dairy produce and foreign policy compliance – at very low cost. German hegemony, it turns our, was exercised in more complicated and indirect ways than is often imagined. The Danes ended the war as members of the United Nations; but for at least three years, they found a comfortable niche in Germany's New Order. (p 103–4)

King Leopold did not leave. He may have been impressed by Germany's treatment of Denmark, but if he hoped for something similar, he was mistaken: Belgium was much more important than Denmark strategically and territorially. (p 106)

Demographers and security experts were also making their contri­bution. In early October 1941, Heydrich made a important program­matic speech about Europe to his colleagues in Prague which marked one of the early signs of the SS's new ambitions for the East: First, he said, there were those countries - Norway, the Netherlands, Flanders, Denmark and Sweden – inhabited by 'Germanic men' 'of our blood and our character', that would be incorporated or associated in some way with Germany. Secondly, there were the Slav countries of eastern Europe; and third, there were the 'spaces' as far as the Urals which would be exploited for their labour and raw materials. Heydrich described a 'German wall' of 'German blood' standing against 'the Asian storm­ flood' (just as Himmler would the following summer to Kersten). (p 207)

German policy in Denmark, on the other hand, showed what could have been done in eastern Europe had the Nazis followed what one disillusioned business executive called 'contenting oneself with the attainable'. The contrast with Poland was scarcely believable. Hitler had said that the Danes should be treated 'in the friendliest manner' in view of their lack of resistance, and as a result business contracts were drawn up 'following normal practices'. What this meant was that the Danes largely ran the economy themselves, through a German-Danish Govern­ment Committee, which enabled the Germans to make extensive but by no means overwhelming use of the country's shipyards, machine-tools plants and other key industries. The Germans trusted the Danes to play along. There was no 'reorganization' of the economy along Nazi Lines, no mass buy up of assets, or plundering of stockpiles and exchange reserves, nor even the forced conscription of labour. Aware of the scepti­cal, not to say hostile, attitude of the Danish public, and anxious to secure continued access to the country's dairy produce, fish and meat, the Germans intervened as little as possible in business transactions. They got what they needed, but, as a result, their share of Danish industrial output probably never exceeded 10 per cent of the total, compared with as much as 30–40 per cent in France. (p 266)

One of the most influential planners was Haushofer. In Geopolitik: Haushofer, Hitler and lebensraum we find:

To be sure, by 1941 Haushofer's theoretical geopolitical constructs had long been drowned out by Hitler's ever-escalating pace of diplomatic crises, war, and extermination. But the general remained true to his convictions to the bitter end: after the Battle of Stalingrad, he penned for Hitler a shopping list of German war aims that included the annexation of Poland, Bohemia, Moravia, Slovenia, Alsace-Lorraine, Eupen-Malmédy, North Schleswig, South Tyrol, Togoland, and the Cameroons; 'friendly' regimes in Finland, the Baltic states, Slovakia, Croatia, Serbia, Greece, Belorussia, and the Ukraine; and a German-dominated 'economic union' with Denmark, Norway, Sweden, Switzerland, and Italy." Geopolitics 'Through the Looking Glass'.

The real goal, if we are to identify just one of several competing concepts, looks indeed more like this Lebensraum:

where the whole of Denmark is simply swallowed up.

Conclusion

While Hitler may have had the most power concentrated into a single hand since Napoleon he was not involved in each and every decision, despite being famous for his micromanagement style for military affairs later on. The multi-headed hydra of the Nazi party had different goals at different times. Keeping Denmark as it was – for the time being – was influenced by Hitler, the racial war concept, racial ideology, power pragmatics and attention spans. As can be seen from different planners and their papers, if Germany had won the war, a little border correction – for the sake of tradition or principle – was by no means off the table.

¹ Mitteleuropa (and German war aims corresponding to that) is a concept that is as constant in German foreign policy as the Russian "drive to warm water ports" like the Dardanelles, if not more so.

Regarding the fate of Denmark in these plans there was ever only one real option:

– Frantz laid out his principal arguments in the late 1840s. Although his posture towards Prussia changed in the coming decades, his main ideas on Central European federalism remained unchanged. The starting point for Frantz's Mitteleuropa vision was a global view of politics in which he foresaw a bipolar global system between the United States and Russia. Given this premise, he argued that only a federally organized Central Europe could withstand pressures from the two great powers. Furthermore, he argued, the federal principle was the only adequate form of government for a united Germany, even under Prussian leadership, since German cultural diversity would neither permit nor survive within a centralized state. For the same reason, it was imperative to unite Mitteleuropa in a confederation in which the Germans would play the role of a 'cultural mediator'

Frantz suggested that Europe be divided into three federations that would cooperate closely with one another in a 'Central European peace union'. Russia, Poland and the Baltic Provinces; the Austrian Empire with the Balkans; and the remaining German states. Eventually the Low Countries, Denmark and Switzerland were to join.' (p 29)

– [WWI aims:] Influenced by the leading banking and industrial circles surrounding Helffrich and Walter Rathenau, Bethmann-Hollweg [Reichschancellor] proposed a Mitteleuropa under German hegemony. Compared with the pan-German programme, it was designed to be a moderate conquest that was, simultaneously, economically necessary. Concretely, the programme demanded the following: the annexation of Longwy-Briey from France, as well as terms of trade that would make France dependent upon Germany (as an Exportland); the preservation of Belgium, which would become a vassal state of Germany (as a military base against England), and the establishment of a Central European economic area under German rule that would include Austria-Hungary, Poland, Denmark, Italy and Scandinavia. (p 44.)

Examples cited from Jörg Brechtefeld: "Mitteleuropa and German Politics 1848 to the Present", MacMillan: London, 1996.