Let's also pause to note that, assuming this site
has its numbers right, Louisiana receives $1.78 in federal funds for every dollar contributed to the nation as a whole.
New Orleans controls the outlet of the Mississippi river, and thus much of the production that flows out the US heartland, and they would be able to charge the US exorbitant transit rates or shut down traffic altogether..
If an independent Louisiana tried that, I'm pretty sure the Union would find some creative ways to make them cut it out, like charging $1,000 for every border crossing. (To say nothing of flat-out invasion and incorporation as a territory without Congressional voting power, like Guam.)