It wasn't arguable at all. The articles of confederation states 'perpetual union' and the constitution says 'a more perfect union.' Every signer of the constitution, including those from the South understood it to be perpetual, as easily revealed by their speeches and letters. There was no question about it. The secessionist doctrine rose later, with Calhoun and is ilk. The whole idea that a state could secede because they don't like the result of an election is absurd, and to say that this was a fact is simply propaganda.
The government was gentle with the South after the war because of the kindness of Lincoln, and because of the political turmoil in the North following his assassination. Lincoln was kind, but was also capable of ruthlessness. Because he practiced his ruthlessness in private and his kindness in public, after his death we were left with one but not the other. The political turmoil came about because Johnson, the Vice President, was a 'war democrat' Lincoln brought on the 'National Union' ticket to win the election of 1864. Without Lincoln, the Republicans felt themselves losing control of the government, against the democrats, with no war to unite them with the republicans, quickly mended their fences between their peace and war wings. The return of southern states to Congress (which Lincoln hastened) further weakened the republican position. When the republicans failed to impeach Johnson, he more or less abandoned his half-hearted attempts at reconstruction, and the southern state governments quickly re-established the old power structure.
When Grant came along after the next election, this was largely complete, and he lacked the inclination to revisit the matter, being more interested in developing the West. Grants stated philosophy was 'If we have to fight, lets get it all over with quickly and then be friends.' Fought he did, and got it over with, and then to him the war was over, and it was time to be friends again.