During World War Two, Hitler removed the Hohenzollern princes from serving in the German Army after he saw the outpouring of grief and sympathy from the German public upon the death of one of the princes while serving in the army. Was the restoration of the Hohenzollern dynasty ever contemplated by the Allied powers or the new German government at the end of the war?
SUMMARY: Because Hohenzollern dynasty and the general conception of Prussia as a kingdom, or Germany as an empire, had already been "destroyed" in minds.
Prussia officially unified the states of Germany and created the Second Reich in 1871, after its successful war against France. This creation was sustained until 1918, when hungry Germans led a riot close to a revolution against the Empire, forcing the Emperor to abdicate and exile in the Netherlands. After a civil war, notably against the communist Spartakists, the Republic of Weimar was installed.
And this is this republic that was overthrown by Hitler in 1933 (technically, there were elections but you know the context of brutal events, lies, and violence as a pressure on the population). The name "Third Reich" was given, after the Second Reich, but Hitler's government and institutions were those of a dictatorship rather than a monarchy: especially, it relied on ideology a lot.
When in 1945 the Third Reich fell, Germany was split in two and the Allies wanted to secure the future from a new German expansion. Installing a new kingdom was certainly not a good idea in that regard. So the Soviets installed a soviet-style republic, the German Democratic Republic, and the Western allies an "Occidental-style" republic, the German Federal Republic.
@totalMongot's third paragraph is a good start. None of the victors wanted a recidivist Germany or even (at the time) a united Germany. Creating a new Kingdom of Germany was for that reason a non-starter.
Additionally, the US did not see any benefit for Germany of a restored Hohenzollern dynasty. The US was staunchly democratic, believed a limited republic to be the best form of government, and so (along with Britain) set up a federal republic for the parts of Germany it controlled -- pretty much the opposite of a centralized kingdom. (The USSR was also anti-monarchy, of course, for its own ideological reasons.)
Beyond that, the original question asks "Why did Germany decide not to restore..." and @Moishe Kohan correctly notes that Germany was not in a position to decide anything even if it had wanted the Hohenzollerns back.
And did any significant number of Germans even want that?
In addition to the other answers, it may also be of interest that even in Germany, few people would have wanted that. (The following points are mostly based on the recent book "Die Hohenzollern und die Nazis" by Stephan Malinowski (https://www.ullstein.de/werke/die-hohenzollern-und-die-nazis/hardcover/9783549100295), which extensively deals with the activities of the Hohenzollerns, in particular the former crown prince, during the 20s and early 30s.)
In the Weimar republic, many people, in particular on the political right, rejected the republic. Additionally, there was a widespread general nostalgia for kingdom(s) and empire. However, there never was a significant political movement for a restoration of the 1871 empire, for various reasons such as
- re-establishing all the (nominally more or less sovereign) states within Germany was unpopular,
- even many people on the right favoured a more egalitarian society without the hereditary privileges of the aristocracy (a notion which had significant racial components in the Volksgemeinschaft),
- and the natural candidates for emperor, former emperor Wilhelm (II.) and former crown prince Wilhelm, were discredited (by the flight to the Netherlands, by their general behaviour during the war and later) among conservative royalists.
So one reason for conservatives (including the Hohenzollerns) for collaborating with the Nazis was to overthrow the republic, with the idea that the house of Hohenzollern may be restored to some kind of reformed imperial throne, but actually, that was never particularly popular even in 1930.
So after the war, a restoration was never seriously considered AFAIK. (Of course, the allies didn't want that anyway.)