It's hard to look back and say with certainty how the vanquished Confederate states should have been treated by the post–Civil War federal government. What can be said for sure is that it was crucial that the South be politically, socially, and economically reintegrated into the United States under its laws, and that those former slaveholding states be required to submit to a certain amount of federal oversight to make sure that the Thirteenth, Fourteenth, and Fifteenth Amendments to the Constitution were being enforced.
Taking a punitive attitude against the already-decimated South would have been counter-productive to Lincoln's own original priority to maintain the cohesion and integrity of the republic. Treating the former Confederacy as a defeated nation would have meant extractive treaties that overextended the federal government's authority, perhaps further weakening the South's path for recovery through reparations or other concessions. The symbolic value of America's dealing with its individual rogue states like a foreign enemy would reflect poorly on the American system and generate more mistrust and resentment from the Southern states, with further armed conflict not unforeseeable.
Treating the Confederacy as sectarian rebels meant that once the extremist ideology motivating their cause—slavery—was formally prohibited, the federal government had legal cause to intervene for enforcement of the federal laws without marginalizing their status as sovereign entities. The ultimate goal was to get newly enfranchised African American men into the body politic as voters, party bosses, and elected leaders, on the way to greater inclusion in mainstream society.