Settle: To determine what is uncertain; to establish; to free from doubt; as, to settle questions or points of law.
Resolve: To arrive at an end by some recognized authority.
If the issues had been settled politically, the outcome would have been a foundation agreed to by all parties and useful for the future. The application of military force, as the supreme recognized authority, caused the parties to arrive at a destination, and the stronger imposed its will on the weaker. The Union never recognized the Confederacy and it never surrendered. Therefore, the mutuality of a settlement was never achieved.
Your last question is one I have not thought about. Ill speculate that the politicians after the Civil War had the same lack of mental energy and moral determination as those before. I doubt they could see much personal profit from thrashing out secession.
The reason why there is no article or section prohibiting secession in the original USC is because it would have never been ratified in the first place.