Quite honestly, OTL is pretty close to as good as you're likely to get, which is strange to say considering the shitshow OTL was, but I think it's true. In many cases, civil wars cripple countries for decades with insurgencies (see: Nigeria and Biafra, or the DRC) and lead to more and more animosity building up over time until the country either splits apart (see: UK and Ireland or North and South Sudan) or goes authoritarian and viciously cracks down on all dissent (See: Chinese and Russian Civil Wars). By comparison, the US got off relatively "lightly," in that after the war Southern separatism disappeared, black people got constitutional protections that were enforced once the political will among a sufficient number of white people existed (and no matter how strong you make these protections, there's no practical way to actually enforce them without major white buy-in, so strengthening them will not in and of itself solve anything), and the paramilitary violence mostly subsided after Reconstruction (barring lynchings of course. See shitshow comment above). There are probably some significant improvements you can make: you might be able to weaken or even avert de jure segregation with the right supreme court ruling (eg Plessy vs Ferguson) but de facto is going to exist without an anachronistically powerful civil rights movement (see: the North in general). You could also plausibly crack down on lynchings, which are clearly illegal and seriously offended the moral sense of a large number of northern whites (although not enough to do much about it for way too long OTL). But I think overwhelmingly and disproportionately white-dominated politics with a de facto black racial underclass is inevitable with any plausible Reconstruction. The US can't militarily occupy the South forever, and if it did you'd end up with the sort of never ending civil war mentioned above.
Much of the discussion around destroying the "planter class" seems to combine Zinn-esque analysis with Maoist policy proposals. The Zinn-esque analysis is the idea that American history is the history of a tiny white economic elite using racism to divide the multiracial working class... which ignores the fact that many "poor whites" enthusiastically joined the Confederacy and fought willingly to preserve slavery, then overwhelmingly supported "Redemption" during and after Reconstruction. Poor white-poor black alliances did happen OTL with the Populists, especially in North Carolina, but didn't last long and generally disintegrated over racism. Blaming the Civil War on exclusively on "the planter class" as a whole and using that to expropriate most or all of them is neither accurate nor just, and will engender massive resistance. You could get away with expropriating a few ringleaders among "the planter class," but most planters are no more guilty of the civil war then most "poor whites." OTL, "planter" dominance disappeared within a few decades anyways, and the result was not racial harmony, since planters were not primarily responsible for racism.
The Maoist policy proposals encompass the uncompensated expropriation of the planters as a class and distributing their wealth to poor whites and their ex-slaves with the intent of destroying them as a class (as opposed to punishing the ringleaders specifically without regard for class). There's a few obvious issues with this:
1) The US was not a Communist state where the very idea of private property and employing people was suspect. Arbitrarily expropriations based on class definitions are not in the cards in any plausible scenario.
2) Most planters were no more responsible then most "poor whites" for the war. Obviously, most of the ring leaders were from the upper class in the South, as is the case for most uprisings, but collective class guilt is not a concept that works well with the US, and plenty of poor whites participated freely and enthusiastically in the war. Expropriating planters to give their lands to poor whites has no real moral justification if you don't accept Communist definitions of class and exploitation.
3) The planters absolutely "have it coming" in the sense that they profited off of slavery for centuries, and you could thus make a perfectly solid moral case for taking their lands and redistributing it to their ex-slaves. But there's two issues with this: first, if you redistribute their lands to their slaves but not to poor whites, that will cause massive resentment, and second, slavery was perfectly legal and not viewed as immoral in and of itself in Southern society prior to the war. Obviously, there were some exceptional people who took a stand against it, and this is not to justify slaver's beliefs in any way, but most people in any society will act in the "mainstream" way, by definition. Attacking planters for acting the way their laws and society told them to act (and even the north was willing to accept, if not love, prior to the war) will engender massive hatred. Expropriating their slaves without compensation (Haiti is the only other country to do this) and shattering their hold over the Federal government is punishment enough.
4) In practice, even if we ignore all the moral and legal issues with expropriating the planter class (and exiling or killing them as some of the more extreme proposals suggest) as a class rather than as individuals, it won't solve anything the medium term. The same thing that happened in Maoist China even after several rounds of land reform will happen in the US: more successful small farmers will start buying up the lands of their less successful neighbors and start turning into large farmers employing people, and pretty soon you'll be back to where you began. The only difference will be that some of these more successful farmers will be black, but (a) most of them will be white, since white people on average will have more education, more experience with finances, better connections, more pre-existing wealth, and better access to the much wealthier white market, and (b) the presence of a minority of successfully black farmers will piss off whites immensely, and the odds of them being driven out/killed/expropriated and their lands and money taken by their white neighbors will rise massively the more visible they are, much like happened OTL when black people got too successful. The Maoist solution to this problem, after failing to solve it with multiple successive rounds of land reform, was collectivization, which had... unintended consequences.
5) Even if we handwave all the legal, moral, and practical issues with doing this, it won't solve the "economic basis of racism" because racism is not a purely economic phenomenon nor solely the fault of the planter elite, despite what Howard Zinn might tell you. As proof, see OTL, where the planter class hasn't been relevant for over a century and yet racism is still here. If anything, the presence of a small black economic elite will engender resentment among both poor whites and their wealthy white competitors.
In short, trying to destroy the "planter class" has no moral or legal basis within the US tradition, will not solve racism or even ameliorate it, will not stop the rise of a new planter class, and will almost certainly engender the sort of long-term resistance present after many civil wars that the US managed to largely avoid OTL. It's a bad idea. Focus on doing OTL Reconstruction better rather than trying to bring a Maoist revolution to the US South.