If the right to vote was like the right to freely speak, or to peaceably assemble, or to exercise religion or to bear arms, then there would be a robust constitutional tradition debating whether this or that law constituted an undue burden on an enumerated right, independent of whether it traduced some other enabling statute. And even the most disfavored classes of persons would retain those rights.
For example, there is a robust history of litigation regarding the rights of prisoners to exercise their rights to free speech and free exercise of religion, in which the debate revolves around just how accommodating a prison needs to be to facilitate the exercise of these rights. By contrast, the overwhelming majority of states deny incarcerated felons the right to vote, and in most states those rights are not even automatically restored upon the completion of the felon’s sentence, even though this disenfranchisement in no way facilitates the operation of the prison system in a safe and efficient manner. No balancing is necessary, because the right to vote is alienable in a way that our enumerated rights are not.
If there were a constitutional right to vote, the Ohio law would surely have been struck down as an unreasonable burden on that right.