From what I have read, Napoleon soundly defeated Prussia and entered a three way negotiation with Russia, Poland, and France after Prussia's defeat.
But those negotiations were mostly between Russia and Napoleon as Prussia was decisively defeated. At this point, Napoleon could have either divided up Prussia with Russia (Polish partition style which Russia had success with).
Another option would have been to either annex Prussia or put someone else on the throne and make it a puppet state. It doesn't seem like there was much Prussia could have done about it.
Instead, Napoleon took some of Prussia's western lands and bullied Prussia around for a bunch of years. But Prussia was still kept around as a political state, and this would hurt Napoleon years later.
Was there good reasoning for leaving Prussia intact?
Well, Napoleon did not just take "some of Prussia's Western lands," the Treaty of Tilsit took away about half of Prussia's pre-1806 territory. In addition to Prussia's Westphalian territories, the Hohenzollerns lost territory to Napoleon's ally Saxony and lost almost all of its gains from the partition of Poland. In the latter case, the newly erected Duchy of Warsaw was a powerful flanking state. The Kingdom of Westphalia, with Napoleon's brother Jerome on the throne, was on Prussia's Western borders. All of this was a serious rearrangement of territory on Napoleon's part, albeit a lot of it was territory had only recently acquired by Prussia, and meant that the rump Prussia had Napoleonic satellite states surrounding it to the east, south, and west.
As to why Napoleon simply did not partition or annex Prussia, this ran counter to Napoleon's policies with regards to satellite states. Napoleon preferred to keep these states highly dependent upon French power and therefore would not let them acquire too much independence. The expansion of the states of Third Germany came under the auspices of the Rheinbund of which Napoleon was its protector and the Kingdom of Westphalia was an important member. The Duchy of Warsaw lacked an actual executive head for its brief existence. It was nominally under a personal union with Frederick Augustus I of Saxony, but the Saxon king did not want to get involved in Polish politics and real power was often in the hands of the French ambassador. Napoleon in his St. Helena memoirs stated he had intended to put Poniatowski on the throne of Poland, but there is little evidence in his actual conduct of diplomacy to suggest he moved beyond toying with the idea of restoring the Polish kingdom.
Furthermore, partitioning and annexation is something easier said than actually accomplished. Rousseau actually noted during the Partitions that Poland might be easy to swallow, but difficult to digest and the course of the nineteenth century bore out this prediction of the great philosophe. The position of Poland within the empire would emerge as a persistent headache for the Russian Empire in the nineteenth century as the Romanov state would not countenance much in the way of any sentiment of Polishness (language, Catholicism, local privileges), especially after the revolts of 1830 and 1861. Dividing and occupying territory often entails upending local elites and power structures that creates problems further down the line.
In short, Napoleon got pretty much what he wanted out of Prussia from Tilsit. Prussia had to pay a large indemnity and keep a small army, and to guarantee these restrictions, it was surrounded by Napoleonic creations. These satellite states themselves were highly dependent upon French power and could thus not stake out policies contrary to the interests of Napoleon. Of course, this created a revanchist sentiment within the Prussian state and many within the Prussian Army waited for the opportunity to redress Tilsit. This speaks to the larger instability of the Napoleonic state system which was fundamentally at odds with the balance of power within the continent.
Sources
Dwyer, Philip G. Napoleon and Europe. Harlow, England: Longman, 2001.
Grab, Alexander I. Napoleon and the Transformation of Europe. New York: Palgrave Macmillan, 2003.
Leggiere, Michael V. Napoleon and Berlin: The Franco-Prussian War in North Germany, 1813. Norman : University of Oklahoma Press, 2002.