Answer why Lincoln was going to further enshrine slavery in constitutional law.
It's a hard argument to claim that what you assert was the cause of the war was going to be much more greatly protected by the man who actually launched the war.
This is a dichotomy that contradicts your claim. If slavery was the cause, then why did Lincoln and all the Northern states offer to protect it further? How do you square that circle?
In any case, it wasn't a done deal: Lincoln couldn't just wave his hand and change the Constitution. And the idea of an unamendable amendment would have had serious problems in the courts. So in the eyes of the secessionists slavery wasn't secure if the slave states remained in the union.
You wrote: "Well this statement presupposes that the issue of slavery had something to do with the cause of the war." Slavery, the spread of slavery to the territories, and the permanence of slavery as an institution had everything to do with the deeper causes of the war -- why the country was so divided and why some people wanted their states to secede from the union, something which no president would allow a state to do unilaterally. So yes, slavery had something -- everything -- to do with the causes of the war.