Brace yourself. Duuring is coming.
Slightly outside of my range, but I'll give it a go anyway:
The entire transformation from Batavian Republic to Kingdom of Holland wasn't a military game, it was political. One must remember that the Batavian Republic and France weren't allies, the Batavians were in a clear vassal-position.
In 1805, Napoleon had already meddled with Batavian politics by appointing Schimmelpennick as head of state, but still he was not satisfied. Basically, he wanted the Netherlands to bow completely down to French rule (For military and economic reasons), and he hoped that by appointing their leader hiself, they would. Schimmenpennick, however, while he did a relative good job, was not to Napoleons liking.
Around the same time, Napoleon was putting his family members on thrones everywhere, and it was time for the Batavians. In early 1806 this had become clear, and the Batavian government of course tried to keep their 'independence' by sending a delegation under Admiraal Verhuell, who was much liked by Napoleon, to plead their cause. Napoleon, however, just send them trough to Louis Boneparte, and it was clear that both the delegation and Louis (Who didn't even want the throne) had no choice. It was clear that the only options were accepting Louis as monarch, or going to war against France, which wasn't a real option.
In short, there was never a real invasion. Just to make absolutely sure everything went to plan, the French army marched in, paraded trough Amsterdam, and left again. Louis was installed to the throne as Lodewijk I, Koning van Holland (King of Holland) and well, there we are.
Of course, plenty of people didn't agree with this, but Louis turned out to be a pretty good king. While Jerome was much disliked and spent lavish amounts of money on his palaces in Westphalia and Joseph was simply kicked out of Spain, Louis became immensely popular with the Dutch by clearing up the mess of a decade of Batavian republicism. When a gunpowdership explosed in the middle of the city, he not just visited the city, he gave money, cloths, send in the army to clear the mess and even send his own personal surgeon to help the wounded, even though Louis had a bad health himself. When there was a major flood, exact same thing. He was nicknamed 'Lodewijk de Goede' (Louis the Good) and for good reason.
Ironically, Louis made the Kingdom of Holland even more independent then the Batavian Republic had ever been. He ignored Napoleons pleas for troops on multiple occasions, refused to install conscription (especially this act was very popular) and pretty much set the entire Continental system aside. The Kingdom wasn't exactly flourishing, but things did became better.
Louis did not want to become a French king of the Dutch, but a Dutch king for the Dutch. He learned Dutch and even made it the official court language (Unlike the courts of the Orange-Nassau who quickly changed that back to French in 1813). Apparently, eventually he got so fed up with Napoleons meddling with Holland, he was making plans to declare war on France and change sides. The army did not support this, however, because they didn't think they could win. Not sure whether that is true, but it's certainly not impossible.
The 'invasion' of the Batavian Republic was the best thing Napoleon probably ever did for the Dutch.
