Why was the Holy Roman Empire not reformed after the Napoleonic Wars?

This is a really complex question, but I'll try to simplify as much as possible.

The Holy Roman Empire as of the Napoleonic Wars was in a parlous state, so much so that it is even hard to define what it was - cue Voltaire's famous quip that it was neither Holy, nor Roman, nor much of an empire. It did not act as a nation-state, but more as an overarching authority (a kind of proto-EU, I suppose you could say.) To that end, it did not have a central government (though there was an occasionally-sitting Imperial Diet in Regensburg), and laws and tariffs were most often decided at a local level. To that end, politically the Holy Roman Empire was often seen by its Habsburg rulers as something of a difficulty. In 1684 an influential civil servant named Philip Wilhelm von Hörnigk published a treatise in which he argued that the Habsburgs should jettison the Holy Roman crown and focus on their core lands in Austria; if they were to do that Austria could become a great power without worrying about having to administer far-flung areas of the empire. In the 18th century, Maria Theresa began far-reaching streamlining and modernisation of internal Austrian bureaucracy, leading her son Joseph II to consider much the same plan that Hörnigk had suggested a century earlier. So, by the 18th century, the Habsburg rulers considered that the most important part of the empire was its core - Austria - and they often saw the complex and myriad states, enclaves and exclaves as being liabilities, not a centre of power. This was largely reflected in literature at the time. Johann Wolfgang von Goethe, in his Faust, included a bawdy tavern song with the like "The Holy Roman Empire, oh poor thing!/How does it stay together?" His contemporary, Friedrich Schiller, had the protagonist of his play Die Räuber advocating the replacement of the empire with a powerful German republic. Goethe and Schiller were early German nationalists, so they had no qualms about an overarching authority over the German states (of which there were approximately 360 at the time.) Their disenchantment with the Holy Roman Empire was that it had almost no political or legal authority to speak of. What they wanted was a nation-state, not a pretend empire.

The death knell of the Holy Roman Empire was, however, the Napoleonic Wars, and this is due to a couple of key factors. For one, the member states of the empire proved unreliable; some voluntarily switched their allegiances to Napoleonic France, while others tried to remain assiduously neutral. For Austria this was especially galling, as it maintained the responsibility for defending the totality of the empire, which stretched its own forces extremely thinly for no discernible benefit. Furthermore, once Napoleon had defeated the Austrians and the Prussians, Germany was remade out of all recognition. I cannot overstate the revolutionary aspect of the territorial reshaping of the region; where once there were 360 German states, by 1815 there were just 37. The Duchy of Württemberg, for instance, was made a kingdom, and its territory and population was doubled nearly overnight, by dint of Friedrich of Württemberg being a supporter of Napoleon. This meant that, while some states and imperial enclaves disappeared from existence, other states (Bavaria, Württemberg, Baden, Saxony, and so on) became so-called Mittelstaaten (literally "middle-states"), which had enough power so as to jealously guard their sovereignty. Napoleon did also (in name at least) create the Confederation of the Rhine, which was to be a bloc of these states, but in practice it never actually happened, as the states themselves dragged their heels over writing so-called "fundamental statutes." Nevertheless, this meant that, by the time the wars ended, the geopolitical outlook in the German region had changed so fundamentally that it could hardly be reversed.

This is not to say that there were not people who wanted a return to the Holy Roman Empire. It is not true that most people thought that Germany should be formed without Austria; on the contrary, a huge number of early German nationalist clamoured for the formation of a German nation-state with Austria at its helm. The advent of the concept of a Prussian-backed Kleindeutschland did not really come about until at least the 1830s, due to the fact that Prussia was deeply unpopular with the Mittelstaaten as a result of its ill-conceived demands that Saxony be annexed to Prussia. After this debacle, Prussia largely withdrew from German politics for several years, in order to deal with its own internal strife. So Austria was seen as the great hope to guide Germany; what German nationalists wanted hearkened back to the Holy Roman Empire, but they wanted a stronger legalistic and constitutional basis for this. The stumbling block was Austria itself. The Austrian minister-president, Clemens von Metternich, saw German nationalism as a dangerous movement that could ultimately dilute Austrian influence. Furthermore, the Habsburgs had finally divorced themselves of the Holy Roman crown, and Metternich felt that any attempted return to the old system would only bring about the same liabilities as Austria had suffered as Napoleon attacked. His solution was the German Confederation: a very loose conglomerate of the German states, with Austria guiding development rather than helming a new nation.

I wish I could give you a more extensive answer, but much of my doctoral thesis revolves around this idea, and I can't very well paste 80,000 words here! But what I really do suggest, if you're interested in the history of the Holy Roman Empire, is that you pick up Joachim Whaley's recent two-volume history of it, published by Oxford University Press. It's a magisterial work, and Whaley deals with the problems and weaknesses of the empire extremely well. Even he, however, struggles with the question of what the empire actually is, which should give you a sense of the problems faced by it in the days of Napoleon.