Blacks were a majority in several parts of the south but a minority nationwide. If you have a violent uprising by blacks in the south to kill all the whites or kill most and keep the rest as slaves, the North would have invaded and killed most of the blacks.
Your situation also ignores the fact that slavery was interracial. In your story, the result of "killing the masters" includes killing a lot of blacks who owned slaves and many Cherokee.
It also involves killing a lot of innocent whites. 3% of whites owned slaves - and yet your story says it is fair that the white farmer treated like crap by rich whites gets murdered and his children enslaved and raped? It is for the sake of those people the Western world would respond with violence.
Suppose the blacks simply killed the whites and the black slave owners, though some would flee. They could try to create a separate nation. Haiti's advantage was the fact that it was an island - it had clear geographic boundaries and was hard to just invade if anyone wanted to take it back. For any black state in the U.S., it would see immediate pressure to reclaim the land on all sides, with many who are familiar with the area. They'd start losing territory immediately.
Another problem is economics and defense. Look at Zimbabwe taking land from successful white farmers and giving it to black subsistence farmers. They went from exporting food to importing food to feed starving people. Same thing would happen when you drive out the organized industrial farmers and exporters and leave only subsistence farming. If left alone, they'd become poor peasant farmers with few skills for industry and no trade.
If they had a violent revolution and weren't violently wiped out as a result, your black state would look like impoverished Haiti, not a developed nation.