A while ago I read somewhere that he had briefly entertained the idea of taking the crown from Francis II and make himself the Holy Roman Emperor, but eventually preferred to make himself Emperor of France. At first sight, this seems strange as he had the power and opportunity to take over the most prestigious title in Europe and an empire that was founded by the French national hero Charlemagne almost exactly a millennium ago. So why didn't he do it?
Additional question: Did Francis II politically outplay Napoleon by not only relinquishing his crown but also dissolving the empire or didn't it matter for Napoleons plans?
To flip the question on its head a bit, what were the benefits of becoming Emperor of the Reich in 1806? Although the HRE title and institutions were stronger than many eighteenth century contemporaries like Voltaire or Frederick II maintained, it was a somewhat archaic and ponderous governmental structure. The dignity and prestige of the title also came with a confusing patchwork of jurisdictions and legal codes. The Reich's defense structure mostly worked as a defensive organization as various regional Kreise provided for a common defense and external wars required a negotiation between the Emperor and the larger principalities, often at the center's loss to the peripheries. Frederick III/I of Brandenburg-Prussia owed his regal title of King in Prussia due to his contributions during the War of Spanish Succession was just one example of how the HRE's various rulers could extract concessions for their imperial sovereign.
None of this was the type of empire Napoleon preferred to rule. While he would reward titles to his lieutenants and allies, it was after they had provided service to his campaigns, not as a precondition. The expansion of regal titles to the middling German states such as Bavaria was an example of this. Similarly, titles often came with territorial enhancement as a means to buy loyalty. Mediatization was a flagrant violation of traditional HRE laws and abandoning the Reich's customs and traditions would make this process easier. The first wave of mediatizations predated the HRE's dissolution in 1802/03 had already set a pattern of rewarding France's loyal German allies with smaller territories, and the the process would be expanded in 1806.
Additionally, Napoleon was very much a man of the Enlightenment and styled himself as a leader truly in touch with modern times. The prestige of the millennial-old imperial title did not outweigh the perception that the HRE was a sickly and outdated state structure. One of the hallmarks of Napoleon's form of government was that the great man was a systemizer par excellence. The HRE's legal codes and structures were many things, but one thing they certainly were not was homogeneous. French decrees towards its allies called for the imposition of various schematic reforms that would allegedly bring central Europe into the modern age. In particular, Napoleon wanted two things from his German allies: taxes and conscripts. Neither one of these resources were items that the states of the old Reich parted with freely, but Napoleon typically never allowed his allies or satellite states the option to refuse his demands.
The structure that Napoleon put in place of the HRE, the Rheinbund, fit the needs of French policy far better than the Reich. By strengthening middle Germany through mediatization and promoting modernization, they provided a useful counterweight against both Austria and Prussia. Napoleon's creation of a whole new bunch of German kings not coincidentally happened after the Austerlitz campaign- brilliantly satirized in the British cartoon Tiiddy-Doll- as not only had the scale of Napoleon's victory given him the ability to redraw the map of Central Europe, but also that Austria's campaign in the summer of 1805 underscored the need for German allies. The Rheinbund states easily fit into this geostrategic need. They were neither strong enough together to forge their own path, nor did the Rheinbund states posses the political unity to form their own bloc. In short, they needed France or another great power to keep their new, elevated status. Additionally, Napoleon saw the Rheinbund, especially the Kingdom of Westphalia under the rule of his brother Jerome, as a means for the French political culture of the Revolution to seep into Central Europe. Napoleon's instructions to Jerome repeatedly stressed that the Germans were receptive to Enlightenment ideas about a rationally-organized state along with admonitions that Jerome was not delivering either the money or troops needed to meet the Empire's demands. Napoleon as the official Protector of the Rheinbund meant he was still deeply involve in German politics, and his power as protector exceeded that of the old Emperor.
This is not to say that Napoleon or people in his government did not toy with the idea of assuming the imperial crown. David's famous painting Napoleon Crossing the Alps featured Charlemagne's name at the feet of Napoleon's horse and Napoleonic propaganda drew explicit parallels between Charlemagne and Napoleon, ranging from Bertrand Andrieu's 1806 bronze medal showing the two in profile or the imperial coronation regalia (crown, the hand of justice, the scepter, and the sword) which were said to have been Charlemagne's or inspired by him. But toying with the idea of assuming the HRE title did not translate into direct action. There was some expectation that after Austerlitz, he would have forced the current emperor to abdicate and receive the imperial title.
Napoleon's general disinterest in the imperial crown beyond idle thinking coupled with Austrian and German decisions to abandon the title to lead to the HRE's ignominious dissolution in August 1806. Even though he was defeated, Francis II recognized that the imperial title did not benefit Habsburg interests. Peace negotiations in the summer of 1806 had banded about the idea of a reformed HRE, but negotiations constantly stalled with the middle German states and the deadlocks over the wider negotiations prompted Napoleon to issue an ultimatum to Francis II to dissolve the Reich. Although the ultimatum gave Francis II a pretext to dissolve the HRE, Austrian state policy had been drifting away from the Reich for some time. Abdicating the title meant none of the middling German states or Prussia could take the electoral title, nor could Napoleon. Even though the dissolution was arguably a breach of imperial law, it strengthened Austria's hand vis-a-vis the middling states by denying them pretenses to up-jumping their regal station.
Napoleon could have undone Francis II's decision had he so desired, but the emerging Rheinbund fit into his designs for Central Europe far better than that of the old Reich. The Rheinbund sanctified France's natural frontiers on the Rhine and the mediatizations provided a precedent to reward (or punish) German allies of France in ways that made them dependent upon their patron. As Protector of the Rheinbund, Napoleon was a Holy Roman Emperor in all but name and unlike the HRE, the middling German states did not have much of a choice in the matter. The Reich's Emperor was an elective office, even though both tradition and realpolitik made it the Habsburg's patrimony. This was an amount of power that Napoleon would not cede to his allies and satellites.
Ironically, the processes that enabled the Rheinbund to succeed the Reich so quickly also allowed for the destruction of French political power in Germany over the course of 1813. The dependency of the Rheinbund states on France's great power status did not preclude them from striking a new bargain with another great power patron. The elevated titles and expanded territory gave German monarchs something that they feared they would lose if Napoleon fell. While this helped keep the Rheinbund viable in a period of French power, this fear became a problem for French power in Central Europe after the wreckage of the 1812 campaign. The German Confederation that emerged after the Congress of Vienna operated similarly to the Rheinbund with Austria, and to a lesser extent Prussia, acting in the role of France as its main patron, albeit with a more equitable relationship between the middling German states and their patrons.
Sources
Forrest, Alan I., and Peter H. Wilson. The Bee and the Eagle: Napoleonic France and the End of the Holy Roman Empire, 1806. Basingstoke [England]: Palgrave Macmillan, 2009.
Whaley, Joachim. Germany and the Holy Roman Empire. Volume 2, The peace of Westphalia to the dissolution of the Reich 1648-1806. Oxford: Oxford University Press, 2012.