Towards the end of his presidency, Ulysses S. Grant, courageous defender of Black civil rights, observed that the 14th and 15th amendments had been a mistake. This not because they had given African Americans citizenship and guaranteed their voting rights, but because the Federal government had no way to actually make these rights a reality. Consequently, the result was basically increasing the political power of the South without actually giving any political power to Black Americans. “They keep those votes, but disfranchise the negroes. That is one of the gravest mistakes in the policy of reconstruction", Grant said sadly.

Indeed, the South received a further 40 extra representatives and votes in the Electoral College. Since the "Solid South" voted as a block, they had oversized influence in National politics, especially the Senate. Moreover, there was no "Solid North" to counter this, as the Democrats could put up credible performances in Ohio, New York and other states while the Republican Party was basically non-existent in the South. First by using terror and violence, and later fraud and the wicked laws of Jim Crow, the South basically reaped the benefit of counting the entire Black population without giving them any votes or influence.

This, of course, was not enough to hand them over complete control of the Federal government. The Republican Party remained dominant in the North, which had greater population and economy. The result was that most Presidents for almost 70 years with the exception of Grover Cleveland and Woodrow Wilson were Republicans. There was no president from the South either, as Wilson, although born in the South, made his career in New Jersey. Most Supreme Court judges and speakers of the House would now be Northern too.

But the South little cared about National politics as long as they were free to maintain White Supremacy in the South. And since the North was unwilling to aid African Americans' in their plight, the region remained an apartheid state where Black Americans had no rights and Jim Crow ruled the day. Ultimately, this meant that the South remained "a oneparty region under the control of a reactionary ruling elite who used the same violence and fraud that had helped defeat Reconstruction to stifle internal dissent. An enduring consequence of Reconstruction’s failure, the Solid South helped define the contours of American politics and weaken the prospects not simply of change in racial matters but of progressive legislation in many other realms."

So, yes, in many ways the failure of Reconstruction assured that the South would keep their power. However, were they more powerful than before? In the ante-bellum, the Republicans held the theory that the South formed a corrupt Slave Power that had hijacked the Federal Government with the purpose of protecting and expanding slavery. The Slave States did have an oversized influence, especially in the Senate and the EC. They kept this after the war, but it cannot be denied that ultimately the Civil War was a disaster for the South, politically, economically and socially. As McPherson details, the Civil War and its end was "a radical shift of political power from South to North":

During the first seventy-two years of the republic down to 1861 a slaveholding resident of one of the states that joined the Confederacy had been President of the United States for forty-nine of those years—more than two-thirds of the time. In Congress, twenty-three of the thirty-six speakers of the House and twenty-four of the presidents pro tern of the Senate had been southerners. The Supreme Court always had a southern majority; twenty of the thirty-five justices to 1861 had been appointed from slave states. After the war a century passed before a resident of an ex-Confederate state was elected president. For half a century none of the speakers of the House or presidents pro tern of the Senate came from the South, and only five of the twenty-six Supreme Court justices appointed during that half-century were southerners.

After the war, the Southern control over the Federal government was irreparably weakened. That's partly why the Radical wing of the Republicans lost strength: there was no Slave Power to fight against anymore, and most Northerners did not care if Southern Blacks were victimized as long as they had control over Washington. Nonetheless, the South remained a united reactionary block that was free to inflict terror and fraud in its Black population and stonewall progress at every level of government. The fact that the entire Black population was counted even though it was disenfranchised helped them in this endeavor. The Southern states were not "more powerful politically than ever before". Long gone were the days when the Slave Power could dictate Federal Policy, when the "Fourth Street Mess" basically threatened the President into doing their bidding and the Supreme Court worked to codify Southern doctrine into law. But it remained powerful, capable of preventing any movements against the White Supremacy they cherished and protected, and the failure of Reconstruction to make sure the civil rights of African Americans were protected is to blame for this.