I think you are underestimating just how much low cunning the South was capable of.
This is why I write such long posts; I like to nail down every possibility. It was my intention as writing it to stress how in fact Jim Crow was allowed to bypass both amendments--and via draconian and grossly biased justice practices use the 13th Amendment loophole for involuntary servitude as a punishment for crime largely evade that one too--which plays neatly into disfranchisement exempt from the 14th amendment representation discount process too since that amendment also says denial of franchise for crime is OK. Rereading your posts it could be read as meaning "better for the South in the long run (and hence the nation)" in that paradoxically, without the grandiose attempt to sweepingly impose universal franchise in one fell but evadable swoop, the grassroots process of fighting the suffrage battles back and forth in the context of the 14th Amendment alone might have concretely led to more tenacious AA enfranchisement--maybe a lot less in the Reconstruction heyday, but the fraction winning it then don't ever lose it and it just expands gradually instead of Jim Crow shoving all Reconstruction gains back. Possibly this is what you meant.
But frankly I read what you wrote as a plain endorsement of the dominant culture assumption, as history was rewritten by Causers and white supremacists, exemplified by the narrative of DW Griffith's
Birth of a Nation, that the USA is basically a white man's country, that the national as well as sectional interest involves prioritizing the interests of the privileged first because in this generally hierarchical world view, elites shall always rule and the rest of us just live to serve in the world they generously or meanly, wisely or foolishly, fashion with their inevitable and natural power. In American context this means de facto white supremacy whatever the fashionability of explicit racism as an ideology; "whites" being first overall the majority, second in possession of a disproportionate share of economic and cultural capital; for others to prosper they must be suitably deferential and pleasing and I read your repeated remarks as a prophecy that African Americans actually getting and keeping the vote would be impossible and therefore striving seriously for it, bad.
I think otherwise. I think it was in the cards in the Reconstruction era to permanently deal in African Americans as regular players in American democracy on the same basis as say American Roman Catholics were eventually normalized. It might have been tactically smarter to just stop with the 14th and 13th Amendments, maybe.
Heck in his inspiring and humane Malê Rising TL Jonathan Edelstein left the freedmen with a surviving Lincoln and no Reconstruction Amendments whatsoever (or maybe just the 13th, I'd have to reread it) and no sustained Federal Reconstruction regime stretching into the latter part of the 1870s either. Reconstruction, insofar as it was a Federal project, was finished before Lincoln's second term ended. OTOH, the state of South Carolina had been taken early by Union power with the heavy assistance of organized self-liberating slave insurgency which ruled on the ground afterward and postwar, took over the SC government with black majority rule. SC never looks back and can defend itself from being terrorized into doing so; AA populations in North Carolina also enjoyed a certain detente. Lacking the paper defenses of OTL African American and their allies fought for civil rights in a long hard slog on the ground, winning results comparable to OTL 1960s by the 1920s.
But the question for this thread is what is the outcome of removing Andrew Johnson, and I think it would be basically good. It is possible for Reconstruction to implode as ingloriously as OTL or even worse, but the more important factor is the resolve of leadership. Johnson occupying the White House frittered away crucial years with inconclusive policy and forced the Radicals later to compensate for damage that a different President would avoid in the first place. With the Radicals having a place at the table and I believe the right on their side, I think we can assume results no worse than OTL overall and quite possibly measurably or even radically much better.
I am defining "good" from a point of view of American mass democracy and the fuller integration of the positive potentials of our humanistic optimism of course, not that of elites disdainful of the masses in any case.
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Meanwhile if you think it did not occur to me that Jim Crow sophistry and ruthlessness would be just as bad without the 15th Amendment as with it, you missed my whole essential point. Which is that the documents don't matter nearly as much as the will, intentions and resolve of the US governmental leadership in this crucial years. True friends of the formerly repressed classes of the south--who were not all black by any means--could, working with them in good faith, leave the states, or enough of them to serve as bastions for the eventual saving of the others anyway, on a basis of solid and self-perpetuating universal suffrage democracy. Enough such friend of the people states in the South, and the subterfuges of the others in denying democracy would first of all be shown as no inevitable outcome of the mere presence of African Americans in great numbers, second the populist Southern states would cooperate with progressive or merely justice oriented interest in the north to put the Jim Crow states in the dock, and at least exact the ruling that what they were doing was undemocratic and also wrong even if the leverage might be lacking to actually compel change for some time. I think the basic dynamic would be for the Jim Crow states to stumble one by one into more radical democracy and once purged of Bourbon style leadership by its own process, never relapse at least not to the extent of suppressing the effective vote of the majority ever again. Eventually the holdout hellholes would be glaringly out of step as such and dealt with on a Federal level, with the support and probably useful advice or even under the major leadership of other Southern states.
It is a matter of whether the Republicans, to be concrete, had any intention of making Lincoln's brave and resounding words at Gettysburg live or not. They were a spectrum of different people; some did, some did not. If we assume the radioactive decay of the inspiring new party with its powerful mandate based on a superior integration of American values into the the poisoned lead of a party of the plutocracy in the Gilded Age was inevitable, then there was a short window of time in which the "golden" aspects of Republicanism, the high idealism rooted in a view that held this to be the proper heritage of all common humanity, might have accomplished the alchemy of laying a sustainable basis for mass and universal democracy in the Southern states before the two parties returned to the sordid business as usual. That is what I would put some hope in, not some proper alchemical formula for the right paper reforms, in this case.
Whereas the repeated apparent hostility your quotes seemed to plainly express against the feasibility or relevance of AA franchise struck me as a product of understandings shaped entirely by that crass system.