The Civil War made succession illegal. The post-war legalities just tidied things up.
You couldn't be more wrong.
First of all, technically the USA never had a civil war. We had a war of secession. It was not even technically a rebellion.
Second of all, there is no provision in the Constitution that allows the federal government to force
states which voluntarily
joined a union to voluntarily
leave that union.
Lincoln and his supporters acted in an unconstitutional manner.
Thirdly, there is no provision in the Constitution for using war as a lawmaking activity. That function is reserved to Congress alone.
That being said, the Confederacy acted in a hotheaded manner and should have pursued their actions in federal court, which, at the time, was very pro-states' rights. Of course, considering that Lincoln threatened the members of SCOTUS and their families with bodily harm if they went against him, it may have backfired and reverted to bellicosity anyway.